# Suppose that 2 ≤ f '(x) ≤ 3 for all values of x. what are the minimum and maximum possible values of f(6) − f(4)?

Answer: If we let m represent the average value of f'(x) over the interval x ∈ [4, 6], then the value of f(6) will be
f(6) = f(4) + m(6 -4)
f(6) = f(4) + 2m
And the difference f(6) - f(4) is
f(6) - f(4) = (f(4) +2m) - f(4) = 2m

The problem statement tells us that m must be in the range 2 ≤ m ≤ 3, so 2m is in the range 4 ≤ 2m ≤ 6.

The minimum possible value of f(6) - f(4) is 4.
The maximum possible value of f(6) - f(4) is 6.

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What value of x makes the equation true? –7.12 = –4.8 + x A. –11.92 B. –11.2 C. –2.32 D. 2.32

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Solve: negative 1 over 2 x 1 = −x 8
a. 7
b. 1 over 2
c. 14
d. 18

Option c - x=14

Step-by-step explanation:

Given : Expression

To find : Solve the expression ?

Solution :

Step 1 - Write the expression,

Step 2 - Take like terms together,

Step 3 - Solve the addition,

Therefore, Option c is correct.

None of these are correct if you typed the problem right. The correct answer would be x=1 over 16

YOU PROBABLY CAN'T ANSWER THIS :/ Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?

Rate of change of the function: 60

Step-by-step explanation:

The exponential function in this problem is

The rate of change of a function between a certain interval is given by

where

is the value of the function calculated in

is the value of the function calculated in

In this problem, the interval is

So we have:

and

Therefore, the rate of change is: