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

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:

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]

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

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]

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.

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

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

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%

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 :)

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

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

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

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

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

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

Is 8/7 a rational number

Answers

Yes.

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

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

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]

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)

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.

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

70,000 inches equals how many miles

Answers

Answer:

1.104798 miles

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!

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!!

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

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:

88 students for 4 classes
what is the unit rate?

Answers

Answer:

22

Step-by-step explanation:

Answer:

22/1

Step-by-step explanation:

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.

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

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