First and Second Derivative Applications

On which of the following intervals is f increasing?

• 
• 
• 
• 
• 

For which value of x is f ' positive and increasing?

• a

• b

• c

• d

• e

Tags

CCSS.HSA.REI.D.10

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

f has a local Max at x = ?

• -2.314

• -1.332

• 0.350

• 0.829

• 1.234

The function f has a local Max at x = ?

• -3

• -1

• 1

• 3

• 4

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Let f be a polynomial function with values of f '(x) at selected values of x given in the table. Which of the following must be true for -2 < x < 6 ?

• The graph of f is concave up

• The graph of f has at least two points of inflection

• f is increasing

• f has no critical points

• f has at least two relative extrema

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

• 
• 
• 
• 
• 

Tags

CCSS.HSA.APR.B.3

Which of the following must be true?

• f is increasing on the interval (0 , 2).

• f is decreasing on the interval (0 , 2).

• f has a local Max at x = 1.

• f has a point of inflection at x = 1.

• The graph of f changes concavity in the interval (0 , 2).

What are the x-coordinates of the Points of Inflection of the graph of f ?

• 0 only

• 3 only

• 0 and 6 only

• 3 and 6 only

• 0, 3, and 6