Applications of Derivatives Review

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.8.EE.B.5

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

Tags

CCSS.HSF.IF.B.4

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

• 0
• -1
• 2
• 5

If a function has a second derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

If a function has a second derivative that is positive, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

• -2
• 0
• 2
• None

What will be true at an inflection point? 

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

 If (a,b) is a local minimum, then what will be true about f''(a)?

• It's postive
• It's negative
• It's zero
• Cannot be determined