Unit #3 Application to the Derivative

How many extrema are in the picture?

• 2
• 3
• 4
• 5

If f"(x) >0, what is true about f(x)?

• it is concave up there
• it has an inflection point
• It's zero
• it is concave down there

If f '(x) >0, what is true about f(x)?

• it is concave up there
• it has an inflection point
• It's increasing
• it is concave down there

If f '(x) <0, what is true about f(x)?

• it is concave up there
• it's decreasing
• It's increasing
• it is concave down there

What will be true at an inflection point? 

• f(x)=0
• f'(x)=0
• f ''(x)=0
• The function is undefined

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

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

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

• before -3 and after 1
• between -3 and 1
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

• 1

• 2

• 3/2

• 1/2

• 1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

• 1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply