Given the function f(x) = 4x3 + 13x, what is the gradient of the function when x = 2 ?

Answers

Answer 1

Answer:

y=45x+115

Step-by-step explanation:

We can find the slope of a line tangent to a curve at a point by evaluating the derivative of the function at that point.

We are given the function

f ( x ) = 4 x 3 + 12 x 2 + 9 x + 7

= f ( x ) = 4 x 3 + 12 x 2 + 9 x 1 + 7 x 0

Using the power rule, let's now compute the derivative of  f( x )

f ' ( x ) = ( 3 ⋅ 4 x 2 ) + ( 2 ⋅ 12 x ) + ( 1 ⋅ 9 x 0 ) + 0 ⋅ 7 x − 1

f ' ( x ) = 12 x 2 + 24 x + 9

We can now find the slope of  f ( x )  at  x = − 3  by substituting this value into f ' ( x )

f ' ( − 3 ) = 12 ( − 3 ) 2 + 24 ( − 3 ) + 9

f'(-3)=12(9)+24(-3)+9

f'(-3)=108-72+9

f'(-3)=45(slope of the tangent line at  x = − 3

Now that we have a slope for the tangent line, we need to identify a point on the line.

We know the tangent line touches the function  f ( x )  at the point  x = − 3 , so let's find the value of  f ( x )  at this point:

f(-3)=4(-3)3+12(-3)2+9(-3)+7

f(-3)=4(-27)+12(9)+9(-3)+7

f(-3)=108+108-27+7

f'(-3)=-20

So we know the tangent line goes through the point

(-3,-20)

Finally, we can use the point-slope formula for a line to find the equation of the tangent line.

y=mx+b

To find the value of  b , substitute the values we have calculated for the point and slope of the tangent line:

(-20)=(45)(-3)+b

-20=-135+b

b=115

So our final answer for the equation of the tangent line is:

y=45x+115

 


Related Questions

What is the slope of the line in the graph?

Answers

the slope is 1

the equation of the line is y=x+1

Your answer
PLS SOMEONE HELP AND NO LINKS PLS

Answers

Answer:

71

Step-by-step explanation:)

What is 73 as a decimal?

Answers

What is 73 as a decimal? answer: .73

Answer

Step-by-step explanation:

find the measure of angle A

Answers

Answer:

so 2x+3x+130=180

so 5x+130=180

5x=50

so 2x =20

3x which is angle a is equal to 30 degree

Answer:

The measure of angle A is 30 degrees.

Step-by-step explanation:

Since all triangles are equal to 180 degrees, you take set up an equation where u add 2x and 3x to get 5x and u add that to 130 and set it equal to 180

2x+3x+130=180 ( combine like terms)

5x=50 (subtract 130 from both sides to isolate our variable which is x)

x=10 (divide both sides by 5 to get rid completly isolate our variable)

Now we know x=10 you can plug that in as our x value so 3x becomes 3*10 which equals 30 which is your answer.

Solve this system of equations by substitution.
y = 4x

2x + y = 6

Answers

blah blah blah multiply input divide
x=1
y=4
Ordered pair= (1,4)

Let f(x) = square root 7x and g(x)= x-5. whats the smallest number that is in the domain of f ° g ?

Answers

check the photos they have the answer

35=11x. i need help

Answers

Answer:

x= 35/11

Step-by-step explanation:

steps

35 = 11x

swich sides

11x = 35

Divide both sides by 11

11x/11 = 35/11

simplify

x = 35/11

4+4 for 100 points brainlyist to first answer

Answers

Answer:

8

Step-by-step explanation:

plz me

Answer:

4+4=8

Step-by-step explanation:

.................

If the center of a circle is
(-5,8) and a point on the circle is (-5, -4) What is the radius?

Answers

Answer:

The radius is 12.

Step-by-step explanation:

You're given the center and a point on the circle. The point and the center both have an x-coordinate of -5, so there is no horizontal distance between them. The distance is only in the vertical direction. The distance from 8 to -4 is 12. Since this is the distance from the center to a point on the circle, this equals the radius.

Joaquin gets paid every Friday. His paychecks for the past 8 fridays were $324, $245.25, $245.25, $245.25, $324,$324,$245.25 and $402.75 find the median

Answers

Answer:

284.625

Step-by-step explanation:

Arrange the numbers highest to lowest.

Find the middle value in the arrangement.

A rectangular garden measures 26ft by 37ft. Surrounding (and bordering) the garden is a path 2ft wide. Find the area of this path. Be sure to include the correct unit in your answer.

Answers

With the 2 ft extra border the garden measure 28x39 = 1092
Without the border. 26x37= 962

1092-962 = 130

The area of this path is 130 squared feet

For the following system, if you isolated x in the second equation to use the subsition method, what expression would you subsitute into the first equation?

2x + y = 8
-x - 3y = -12

A. 3y + 12
B. -3y + 12
C. 3y - 12
D. -3y - 12​

Answers

A.3y+12

i think so,or maybe D or B

what is the approximate length of hypotenuse with a 35 degree angle and one leg is 12

Answers

Answer:

37

Step-by-step explanation:

35^2+12^2=37

1. Which of the following sets of integers is arranged in order from LEAST to GREATEST?
Oi-1.5 - 9
O (1. - 5. - 10)
O (12. - 8,0)
O { - 13. - 12,9)

Answers

Answer:

Last option:

(-13, -12, 9)

Step-by-step explanation:

Here you need to look at a number line.

(an infinite line with the zero in the middle, at the left we have the negative numbers which increase to the left, and at the right, we have the positive numbers that increase to the right)

for any two pair of numbers in the number line, the number at the right is larger than the number at the left.

So for example, -10 is at the left of -3

Then:

-10 < -3.

Then a set is ordered from least to greatest if:

first we have the largest negative numbers

then the smaller negative numbers

then the zero (if there is a zero)

then the smaller positive numbers

then the largest positive numbers.

The only set that meets this condition is the last one:

(-13, -12, 9)

Why the others not meet this condition?

in the first one we have -9 after 5, and we know that -9 < 5

in the second one we actually have an order from greatest to least.

in the third one we have -8 at the right of 12, and we know that -8 < 12

A check cashing service found that approximately 5% of all checks submitted to the service were fraudulent. After instituting a check-verification system to reduce its losses, the service found that only 45 checks out of a random sample of 1124 were fraudulent. Does this sample provide sufficient evidence at the .01 significance level that the check verification system is effective

Answers

Answer:

Pvalue of the test is 0.0618 > 0.01, which means that this sample does not provide sufficient evidence at the .01 significance level that the check verification system is effective.

Step-by-step explanation:

A check cashing service found that approximately 5% of all checks submitted to the service were fraudulent.

This means that the null hypothesis is:

[tex]H_{0}: p = 0.05[/tex]

Test if the check verification system is effective:

If it is effective, the proportion will decrease, so we are going to test if after the change the proportion is lower than 0.05, that is:

[tex]H_{a}: p < 0.05[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.05 is tested at the null hypothesis:

This means that

[tex]\mu = 0.05[/tex]

[tex]\sigma = \sqrt{0.05*0.95}[/tex]

After instituting a check-verification system to reduce its losses, the service found that only 45 checks out of a random sample of 1124 were fraudulent.

This means that [tex]n = 1124, X = \frac{45}{1124} = 0.04[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.04 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{1124}}}[/tex]

[tex]z = -1.54[/tex]

Pvalue of the test and decision:

Probability of finding a sample proportion lower than 0.04, which is the pvalue of z = -1.54.

Looking at the z-table, z = -1.54 has a pvalue of 0.0618.

Pvalue of the test is 0.0618 > 0.01, which means that this sample does not provide sufficient evidence at the .01 significance level that the check verification system is effective.

I don’t know somebody help me

Answers

Answer:

C baybee

Step-by-step explanation:

they are the same angle and they are found in the inside making it alternate interior

Answer:

B

Step-by-step explanation:

Test Pythagorean Theorem
> Chemistry: Periodic Table of Elen
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Unit Test: Pythagorean Theorem
UNIT TEST:
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ABCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 14 centimeters.
What is the length of the other leg?
Enter your answer, as a decimal rounded to the nearest tenth, in the box

Answers

Answer:

11.31 cm

Step-by-step explanation:

you got the k12 link to

plus you wanna get on my animal crossing island

the dodo code is 98GVY

PLEASE ANSWER ILL GIVE YOU BRAINLIEST

Answers

Answer:

i think its 28.27

Step-by-step explanation:

Step-by-step explanation:

[tex]v \: = \: pi \: \times \: r {}^{2} \: \times h[/tex]

Volume = 3.14×2.25×4 = 28.26 yd³

I need help please. aaaaaannnnnnnnndddddddddd thannkyou

Answers

Answer:

7:58

Step-by-step explanation:

The little hour hand is a bit past the 7. The long minute hand is closest to 12, which is 60 minuets. Just look the the mark that the little hand points at.

would anoyone be willing to help

Answers

Sure, what do you need help with?

t = p + 50
The variable p represents the number phone calls she routes, and the variable t represents
the number of minutes she is on the phone. In all, how many phone calls does Shivani have
to route to spend a total of 93 minutes on the phone?

Answers

The only way i can think of working out this question is this:

t = time p = phone calls

insert what we know:-

93 = p + 50

make P on its own:-

take away 50 from each side

43 = p

switch (you don’t HAVE to do this) :-

p = 43

So, shivani has to route a total of 43 phone calls to spend a total of 93 minutes on the phone.

Two sets of parallel lines intersect as shown. Given ∠2 = 130° what is ∠9?

Answers

Answer:

50 degrees. The angle is the opposite of angle 9, making it 180-130=50.

I need help.



The x-intercepts of the graph of a certain parabola are (0,0) and (10,0).
The axis of symmetry is x =

Answers

Answer:

the symmetry would be the opposite

Step-by-step explanation:

hope it helps

Can someone please explain to me how to do this

Answers

Answer:

-7

Step-by-step explanation:

-9(x+3)=36

-9x-27=36

-9x=36+27

-9x=63

-9x/9=63/9

x=-7

Share R600 amongst Tom, Paul and Anne in the ratio : 3:4:5 respectively.​

Answers

Step-by-step explanation:

Total Shares = 3 + 4 + 5 = 12 shares

12 Shares = R600

(12÷12) Share = R(600÷12)

1 Share = R50

(1×3) Shares = R(50×3)

3 Shares = R150

4 Shares = R(50×4) = R200

5 Shares = R(50×5) = R250

Tom Gets R150.

Paul gets R200.

Anne gets R250.

Can somebody please help me!!!!!

Answers

Answer:

Varies

Step-by-step explanation:

What this question is asking you to do is to measure the angle of the blue dot and find the 90 degree angle, so you need to get a protractor and measure the 90 degree angle in order to get the answer

Answer:

Step-by-step explanation:

Exercise 11.1.2: Find the next permutation in lexicographic order. About For each permutation of {1, 2, 3, 4, 5, 6, 7}, give the next largest permutation or indicate that the permutation is the last one in lexicographic order. (a) (1, 2, 3, 4, 5, 6, 7) (b) (7, 6, 5, 4, 3, 2, 1) (c) (1, 7, 6, 4, 2, 3, 5) (d) (3, 7, 6, 5, 4, 2, 1) (e) (5, 4, 7, 6, 3, 2, 1)

Answers

Solution :

A permutation in the field of mathematics may be defined as the arrangement of its members into a linear order or a sequence. However, if a set is already being ordered, then it is the rearrangement of the elements of the set.

In the context, the next largest permutation set is :

a). (1,2,3,4,5,6,7)

b). The given permutation is the last one in the lexicographic order.

c). (1,7,6,4,2,5,3)

d). (4,1,2,3,5,6,7)

e). (5,6,7,4,3,2,1)

The next permutation in lexicographic order will be (5,6,7,4,3,2,1).  

What is a permutation?

It should be noted that a permutation in the field of mathematics where there are several possible ways in which numbers or things can be ordered or arranged.

When applied to numbers, the lexicographic order is increasing numerical order. This is an increasing numerical order from left to right). For example, the permutations of {1,2,3} in lexicographic order are 123, 132, 213, 231, 312, and 321

In the context, the next largest permutation set is (5,6,7,4,3,2,1).

Learn more about permutations on:

https://brainly.com/question/1216161

two primes that add to 24

Answers

Answer:

11+13

Step-by-step explanation:

because of math boom

What is the domain of the function

Answers

The answer is -2,2,3,4

Which of the following are ordered pairs for the equation y = 1/2x + 2?

Answers

Answer:

Some ordered pairs could be (0,2) and (2,3).

Step-by-step explanation:

Hope this helps!!

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