Curve Sketching

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

• f(x) is increasing

• x=-1, 1, 2

• f(x) is concave down

• x=-2

• f(x) has a local max

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

• (-3,-1) and (1,2)

• f(x) has a point of inflection

• [-3,-2] and [0, 3]

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

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

Groups:

(a) True

,

(b) False

• f is concave up on (2,4)

• f(x) has 3 P.O.I.

• f is never concave down

• x=5 is a local minimum

• f is increasing on [1,5]

• f(x) has 2 relative extrema

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

• x=-2, 1

• g has a point of inflection

• x=-1, 6

• g has relative extrema

• (-2, 3)

• g is decreasing

• x=-2, 3

• g'' is undefined

• [-1,6]

• g is concave down

Tags

CCSS.HSF.BF.B.3

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

What are all intervals on which the graph of f is concave down?

• -1 < x < 1

• 0 < x < 2

• 1 < x < 3 ONLY

• -2 < x < -1 ONLY

• -2 < x < -1 AND 1 < x < 3

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

• x=-1 and x=4
• x=-3
• x=1
• x=3

List all of the x-locations of the points of inflection of the function whose derivative is graphed.

• {-4, -2, 0}
• {-2, 0}
• {-2, 0, 1}
• Cannot be determined

List all of the x-locations of the minimum points of the function whose derivative is graphed.

• {-2, 1}
• {-1, 1}
• {-1}
• Cannot be determined}