Concavity & Second Derivative Test

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

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

What will be true at an inflection point?  (select the best answer)

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

Where is the relative maximum of  $f\left(x\right)=x^3-3x^2-1$  on the interval [-3, 2]?

•  $x=0$  

•  $x=-1$  

•  $x=2$  

•  $x=5$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

On what interval(s) is the function  $f\left(x\right)=x^3+6x^2$ concave down? 

•  $\left(-\infty,-4\right)$ 

•  $\left(-\infty,-2\right)$  

•  $\left(-2,\infty\right)$ 

•  $\left(0,\infty\right)$ 

Where is the point of inflection for the function  $f\left(x\right)=x^3+6x^2$  ?

•  $x=0$  

•  $x=-4$  

•  $x=-2$  

•  $x=2$  

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None
• x = 0
• x = 0, 2
• x = -2, 0, 2

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None
• x = 0
• x = 0, 2
• x = -2, 0, 2