ap calc review ws 86-89

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

In the following picture, what does the

 $+$  
mean about the graph of  $f\left(x\right)$  

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is positive

•  $f\left(x\right)$  is negative

Consider the  $f'\left(x\right)$  sign chart.  What can you conclude about the point  $x=2$  on  $f\left(x\right)$  ?

• local maximum

• local minimum

• stationary point/platuae point

f''(x) is pictured. Which x values are inflection points of f(x)?

• x=-5 and -1
• x=-3
• x=4
• no inflection points

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

7.

• (A)

• (B)

• (C)

• (D)

f' is given, which could be f?

• A
• B
• C

Which of the following statements must be true?

I. f has a relative Min at x=-3.

II. The graph of f has a point of inflection at x=2.

III. The graph of f is concave down for 0 < x < 4.

• I only

• II only

• III only

• I and II only

• I and III only

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5