Calc Applications of Derivatives

Let f be the function given by f(x) = x³.  What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [-1, 2]?  (No calculator)

• 0 only
• 1 only
• √3 only
• -1 and 1

If   $x=0.5$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \cos^2x\cdot\ln x$  then  $x=0.5$  is a 

• local maximum

• local minimum

• neither

Tags

CCSS.HSF.IF.C.7

• 1/2
• -1/2
• 0
• 3/2

Critical numbers occur where the first derivative is what? (Check all that apply).

• endpoint

• zero

• maximum

• undefined

Tags

CCSS.HSF-LE.A.1B

What is the value of a if f has a local minimum at x=4?

 $f\left(x\right)=6x^2-ax^3$  

(a)  

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

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

• 
• 
• 
• 
• 

Tags

CCSS.HSA.APR.B.3

The function f has a first derivative

 $f'\left(x\right)=x\left(x-3\right)^2\left(x+1\right)$  
At what values of x does f has a relative max? No Calculator

• -1 only

• 0 only

• -1 and 0 

• -1 and 3

• -1, 0 and 3

Let

 $g\left(x\right)=2x^{3\ }-3x^2-12x+18$  
On which interval is g both decreasing and concave up?

• (- $\infty$  , -1)

• (-1, 1/2)

• (-1, 2)

• (2,  $\infty$  )