AP Calc AB Review for QZ 17-18

What are the conditions that satisfy the Mean Value Theorem, and what does it mean?

Tags

Mean Value Theorem

What is the average rate of change of the function $f$ over the indicated interval?

$f\left(x\right)=x^2-3x-28,\ \left[-4,7\right]$

• 0

• 11

• 6

• 66

Tags

average rate of change

What is the derivative of

$f\left(x\right)=x^2-3x-28$ ?

• $2x-3$

• $2x+3$

• $x-3$
  

• $2x^2-3x-28$
  

Tags

derivative of polynomial

What is the x-value at which the function below has the same slope as the average rate of change over the indicated interval?

$f\left(x\right)=x^2-3x-28,\ \left[-4,7\right]$

• 1.5

• -1.5

• 0.5

• -0.5

Tags

Mean Value Theorem

What is the average rate of change of the function below over the indicated interval?
$f\left(x\right)=12\sqrt{x}$ , [1, 16]

• 12 / 5

• 1

• 0

• 36

Tags

average rate of change

What is the derivative of
$f\left(x\right)=12\sqrt{x}$ ?

• $6\sqrt{x}$

• $\frac{6}{\sqrt{x}}$

• $12\sqrt{x}$

• $\frac{12}{\sqrt{x}}$

Tags

derivative techniques

What is the x-value at which the function below has the same slope as the average rate of change over the indicated interval?
$f\left(x\right)=12\sqrt{x}$ , [1, 16]

• 2.5

• 6.25

• 14.4

• 6

Tags

Mean Value Theorem

What is the average rate of change of the function below over the indicated interval?
$f\left(x\right)=\frac{x-4}{x+1}$ , [1, 4]

• 0.5

• -0.5

• 2

• -2

Tags

average rate of change

What is the derivative of
$f\left(x\right)=\frac{x-4}{x+1}$ ?

• $f'\left(x\right)=\frac{5}{\left(x+1\right)^2}$

• $f'\left(x\right)=\frac{-3}{\left(x+1\right)^2}$

• $f'\left(x\right)=\frac{2x-3}{\left(x+1\right)^2}$

• $f'\left(x\right)=\frac{2x+5}{\left(x+1\right)^2}$

Tags

derivative techniques

What is the x-value at which the function below has the same slope as the average rate of change over the indicated interval?
$f\left(x\right)=\frac{x-4}{x+1}$ , [1, 4]

• $-1+\sqrt{10}$

• $-1-\sqrt{10}$

• 4

• 2

Tags

Mean Value Theorem