Homework #13 (AP Calc$)

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum

What is the relative maximum value?

• y = 4
• y = 2
• y = 1
• y = -1

Identify the critical points of the following function: $g(x)=2x^3-3x^2$  

• x = -1,1

• x = 0,0

• x = 0,-1

• x = 0,1

Find the derivative of the given equation

f(x) = x³ + x² + 3

• 3x² + 2x

• 3x + 2x

• 3x + 2x + 3

• x³ + x²

Find all the critical numbers of

f(x) = 2x³ – 6x² + 12

Select ALL that apply.

• x= 4

• x= 0

• x= -2

• x= 2

 $f\left(x\right)=\frac{2}{3}x^3-6x^2+16x+14$  
Find the critical numbers of f(x).   Select ALL that apply

• x=2

• x=0

• x= -4

• x= -2

• x = 4

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Which of the following could be the graph of f ' , the derivative of f ?

• 
• 
• 
• 
• 

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

• 0
• -1
• 2
• 5