Derivative Graph Analysis

Given this graph of f'(x), match the correct interval to what is happening with the function f(x).

• f(x) is concave up

• x=-1, 1, 2

• f(x) has a local max

• [-3,-2] and [0, 3]
• f(x) has a point of inflection

• (-3,-1) and (1,2)

• f(x) is concave down

• (-1,1) and (2,3)
• f(x) is increasing

• x=-2

Given this graph of f'(x), select all values where f(x) has a point of inflection.

A function is increasing when ​f'(x) ​ (a)   ​ ​

A function has a local maximum when f'(x) ​ (b)  

A function has a point of inflection when f'(x) ​ (c)  

A function is concave up when f'(x) ​ (d)  

• changes from positive to negative
• changes from negative to positive
• is positive
• is negative
• has a local extrema
• is decreasing
• is concave up
• is concave down.
• is increasing

Based on this f'(x), categorize each statement as true or false.

Groups:

(a) True

,

(b) False

• x=5 is a local minimum

• f is concave up on (2,4)

• f(x) has 2 relative extrema

• f is never concave down

• f is increasing on [1,5]

• f(x) has 3 P.O.I.

Given the function g'(x), Make each statement TRUE!​

g(x) has a ​ (a)   at x = 0,2,3

because g'(x) ​ (b)  

• point of inflection
• relative max
• relative min
• has relative extrema
• is increasing
• is decreasing
• has a slope of 0

Given the graph of g'(x), Match the following characteristics.

• x=-1, 6

• g is concave down

• [-1,6]

• g has a point of inflection

• (-2, 3)

• g'' is undefined

• x=-2, 1

• g has relative extrema

• x=-2, 3

• g is decreasing