Mathematics College

If f(2) = 12 and f '(x) ≥ 3 for 2 ≤ x ≤ 5, how small can f(5) possibly be?

Answers

Answer 1

Answer:

21

Step-by-step explanation:

From our previous knowledge, if f'(x) = m ,

Then f(x) = mx+c

For a smaller value of f(5), m should be the smallest possible integer if m = 3

i.e. f(x) = 3x+c

replacing the value of x with 2 given from the question to get the value of c, we have:

f(x) = 3x+c

f(2) = (3×2)+c

where; f(2) = 12

12 = 6+c

- c = -12 + 6

- c = - 6

c = 6

Now, f(x) can now be;

f(x) = 3x + 6

f(5) = (3×5)+6

f(5) = 15 + 6

f(5) = 21

Therefore, smallest possible value of f(5) is 21

Related Questions

Solve for p in the literal equation 8p+5r=q

Answers

8p + 5r = q

We have to isolate the variable  p. Let's begin by subtracting 5r from both sides.

8p = q - 5r

Divide both sides by 8

p = [tex]\frac{q - 5r}{8}[/tex]

[tex]8p + 5r = q[/tex]

Subtract 5r on both sides of the equation.

[tex]8p = - 5r + q[/tex]

Divide both sides of the equation by 8.

[tex]p = \frac{ - 5r + q}{8} [/tex]

Lifelike Studios charges a one time sitting fee to take your photograph, then adds 50 cents for each photograph you order. Based on the information given in the graph, how much does Lifelike Studios charge for the sitting fee?

Answers

Sorry I am not sure

What is 2 times 300=? Just kidding i know the answer but any body wanna just talk?

Answers

Answer:

Sure! XD

Step-by-step explanation:

600:) hope I helped ya out

70,000 inches equals how many miles

Answers

Answer:

1.104798 miles

Mike and Julie are making slime. The table shows the number of drops of blue food coloring and the number of drops of red food coloring they use in each batch Drops of Food Coloring Number of blue drops Number of red drops 20 4 40 8 60 12 80 16 What is the constant of proportionality of the ratio of the number of blue drops used to the number of red drops used? 0.2 0.5 2 5

Answers

Answer:

5 drops

Step-by-step explanation:

Which expressions are equivalent to k/2 ?

Answers

Answer: (1/2)k

Step-by-step explanation:

Answer:

1/2 kand k/2

Step-by-step explanation:

Mr. Andrews is trying to lose weight. He starts the year weighing 254 pounds. If he plans to burn enough colories to lose 4 pounds per week, then how many weeks will poss before Mr. Andrews weighs 228 pounds? Variable: bit bin Solutions​

Answers

Answer:

6.5

Step-by-step explanation:

it will take Me. andrews 6.5 weeks to get to 228 pounds

How many more dollars will you spend if you buy 12 cookies at Charlie’s Cookies instead of buy 12 cookies at Sam’s?
Sam’s cookies 6 $8.00 Charlie’s cookies 4 $7.00

Answers

Step-by-step explanation:

Sam's cookies = $16 for 12

Charlie's cookies = $21 for 12

$5 more when buying Charlies other than Sam's

Determine whether f(x) = 3x + 1 and g(x) = (x-1) / 3 are inverses functions. Group of answer choices There are not inverses since both composition equal x. There are inverses since both composition equal x. There are inverses since both composition equal x + 1. There are not inverses since (f (g(x)) = x + 1

Answers

Answer:

They are inverses since both composition equal x.

Step-by-step explanation:

Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.

Let's look for the inverse of f(x).

Given f(x) = 3x+1

Let y = f(x) so that y = 3x+1

Replace y with x

x = 3y+1

Make y the subject of the formula of the resulting equation;

3y = x-1

y = (x-1)/3

The new function of x will be the inverse of f(x)

Hence f^-1(x) = (x-1)/3 = g(x)

Another way to check is to find their composition. Let's find f(g(x) and g(f(x)

F(g(x)) = f((x-1)/3)

Replace x with (x-1)/3 in f(x)

F(g(x)) = 3[(x-1)/3]+1

F(g(x)) = x-1+1

F(g(x)) = x

Similarly for g(f(x));

g(f(x)) = g(3x+1)

Replace x in g(x) with 3x+1

g(3x+1) = (3x+1-1)/3

g(3x+1) = 3x/3

g(3x+1) = x.

Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions

which expression is equivalent to -4.5-6.2y​

Answers

Answer:

the answer is 6.2y-4.5

Step-by-step explanation:

Answer:

the answer is A. -6.2y - 4.5

Step-by-step explanation:

got it right on edge, i hope this helps.

4c-d for c please help!

Answers

Answer:

c=d/4

Step-by-step explanation:

we have to get c by itself...first we have to add d t the other side of the equation so

4c=d now since 4 is being multiplied by c we have to divide it out.

c=d/4

find the midpoint of the segment with the following endpoints (8,7) and (5,4)

Answers

The midpoint is (6.5, 5.5)
(X1-X2)/2 = 8-5/2 = 1.5

(Y1-Y2)/2 = 7-4/2 = 1.5

Now add (1.5,1.5) to (5,4) u get the mid point (6.5,5.5)

Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?

Answers

Answer:

80

Step-by-step explanation:

20 / 25 = 0.8 = 80%

Answer:

80%

Step-by-step explanation:

20/25 = 0.8 = 80%

Is 8/7 a rational number

Answers

Yes.

8/7 (1 1/7) is rational.

13/24 × 3 5/9 multtplying fraction help​

Answers

Answer:

31/6

Step-by-step explanation:

Step 1:

13/24 × 3 5/9

Step 2:

13/24 × 32/9

Step 3:

62/12

Answer:

31/6

Hope This Helps :)

Round to the nearest ten thousand: 324,799 pls help I dont know how 2 right it​

Answers

Answer:

It is 300000...........

Answer:

300,000+20,000+4,000+700+90+9

Step-by-step explanation:

Your welcome!!

Find Slope (3,-4)and(9,-4)

Answers

Slope is undefined as the answer is 6/0

Answer:

The slope is zero (0)

Step-by-step explanation:

-4-(-4)/ 3-9

0/-6

0

1) Given the following problem: I am thinking of a number. If you double the number and add 10, the result is 22.

What is the number?
a) Write a detailed explanation of the solution of the problem using the problem solving strategy: Work Backwards

Answers

Answer:

the number is (((6))))

Answer:

The answer is 6

Step-by-step explanation:

What wanna start out with finding the difference by subtracting 10 from 22. This would give you the difference of 12. Since its 'double the number', we are going to find the quotient of 12 / 2 = 6. You will then end up with the answer 6.

25x - 10y = -35


Helpppp

Answers

Answer: x = 1 y = 6

Step-by-step explanation: 25x1=25, -10x6= -60, 25-60=-35.

Have a great day!

What is the Area of the letter E

Answers

Answer:

24 square inches. do the area of the whole rectangle (7x12) and subtract the two little rectangles (5X6) x 2= 60 so 84-60=24

Step-by-step explanation:

What is 8,541 rounded to the nearest thousand?
A) 8,500
B) 8,000
C) 8,600
D)9,000
ANSWER PLEASE

Answers

D. 9,000 hope this helps

Step-by-step explanation:

Answer:

Question What is 8,541 rounded to the nearest thousand? Answer D)9000

Your Welcome =)=}[tex]\sqrt{x} 8\\[/tex]

Solve for E.

h=E/mg​

Answers

Answer:

hmg = E

Step-by-step explanation:

Step 1: Write equation

h = E/mg

Step 2: Multiply both sides by mg

hmg = E

Cricket match Australia v England begins 10:00 UK time. Australian time is 11 hours ahead of UK time. What time will the game start in Australia (24 hr clock)

Answers

Answer:

Step-by-step explanation:

21:00 i believe

Levi earned $489.90 at his job when he worked for 23 hours. What was his hourly wage, in dollars per hour? (HELP!!!!)

Answers

$489.90 divided by 23 = dollars per hour = $21.30

Name a number greater than 1 that is both a perfect square and a perfect cube. Explain how you know this.

Answers

Answer:

64

Step-by-step explanation:

64 is both a perfect square and a perfect cube.

8*8=64

4*4*4=64

Answer:

hello!

Step-by-step explanation:

lets solve this,

64.

8x8= 64.

4x4x4= 64.

need help, Will give brainliest

Answers

Answer: X=2

Explanation:

3x-5=1
Plug in the variable

3(2)-5=1
Multiply 3x2

6-5=1
Subtract

ca
7. Consider the equation a-3 =
What value(s) of a make the equation true?
(3)?

Answers

It’s true because of the a

If g(x) = 10 + 2x what is g(-3)

Answers

Answer:

4

Step-by-step explanation:

[tex]g(x)=10+2x\\\\g(-3)=10+2(-3)\\\\g(-3)=10+-6\\\\g(-3)=10-6\\\\\boxed{g(-3)=4}[/tex]

Hope this helps.

If you sub in -3 for x, and add it all up it’ll be 4

HELLLP!!!!!!!!!!! PLS

Answers

Answer:

3 * 4/4 = 12/4

12/4 + 1/4 = 13/4

One fraction:   13/4

Mixed number  [tex]3 \frac{1}{4}[/tex]

88 students for 4 classes
what is the unit rate?

Answers

Answer:

22

Step-by-step explanation:

Answer:

22/1

Step-by-step explanation:

Other Questions
2. Antes de empezar una carrera relacionada con el medio ambiente, Ud. tendr que mostrar que es responsable en cuanto a cuidar el planeta. Qu acciones especficas podr comenzar a practicar ahora para preservar y proteger el medio ambiente y el planeta? Recuerde que cada accin que Ud. haga, sumada con las acciones de los dems, beneficia el futuro de todos. Use el tiempo del futuro inmediato (voy a +infinitivo), y escriba y despus grabe 5 oraciones diferentes. (20 puntos) Modelo: Voy a reducir el uso de mi coche y caminar ms o usar transporte pblico. What am I doing wrong in step 5? A small scale map shows Pablo's retirement party will cost $8 if he invites 4 guests. If there are 6 guests, howwill Pablo's retirement party cost? Solve using unit rates. Carbon oxygen cycle and rainforest in a sentence There are 4 consecutive integers that have a sum of 34. What are the integers 2. Which of these graphs represents a function? Read each incomplete sentence and choose the option with the correct verbs to complete them.Claudio ________ mojado. Las toallas ________ secas para Claudio. es; son est; estn son; est soy; es Whats -86.4 divided by 3.2 Read the passage. In Mayan cities, the most important buildings were constructed around a plaza, or open area, in the center of the city. Common people, or workers and farmers, had their homes on the edges of the city. The most important and valued people, such as priests, government leaders, and skilled workers, lived in the center. Also in the center of the city were the buildings that citizens needed access to, such as places of worship and governmental buildings. Some places of worship were also built near the center of the city. What is the central idea of the passage? Temples in ancient Mayan cities were open to all people. A central plaza was the most important place in Mayan cities. Government buildings were the largest structures in Mayan cities. Homes for Mayan workers were located near the citys plaza. A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?Type your numeric answer and submit If the temperature in Texas dropped 35 degrees in 7 hours on Tuesday. What is the change over time? I need help in the simplest way! Use the digits 1-5 to make the smallest whole number possible. Write your answer in standard, expanded, and word form. Who did Marqus de Rub want to gain as allies against the Apaches?a. the Comanches b. the British colonies c. the French d. the Lipan Apaches Please select the best answer from the choices provided A B C D For questions 12-17, determine whether each statement is always, sometimes, or never true.12. TQ and QT are the same line. 13. JK and JL are the same ray. 14. Intersecting lines are coplanar.15. Four points are coplanar.16. A plane containing two points of a line contains the entire line.17. Two distinct lines intersect in more than one point. simplify 1/3(6x12)+4x whats the answers? to this The table below shows the total cost of buying printer ink cartridges for both members and nonmembers of a shopping club. Price of Ink at Shopping Club Number of ink cartridges purchased Total cost for members (with membership fee) Total cost for nonmembers 0 $30 0 1 $40 $25 2 $50 $50 3 $60 $75 Which statement is supported by the table? Trapezoid ABCD is reflected over the line y - x. What rule shows the input and output of the reflection, and what is the new coordinate of A (1 point)B0A(X,Y)--(-x): A is at (1,5)(X,Y) (YX); A' is at (1-5)(x,y)--(-x,y); A' is at (5, 1)(x,y)--(-X, "): A' is at (5, -1)