5-7 The Second Derivative Test

5-7 The Second Derivative Test

Guided Note

Multiple Choice

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

•  $x=0$  

•  $x=-4$  

•  $x=-2$  

•  $x=2$  

Multiple Choice

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

•  $\left(-\infty,-4\right)$ 

•  $\left(-\infty,-2\right)$  

•  $\left(-2,\infty\right)$ 

•  $\left(0,\infty\right)$ 

Multiple Choice

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

•  $x=0$  

•  $x=-1$  

•  $x=2$  

•  $x=5$  

Multiple Choice

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

Multiple Choice

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Multiple Choice

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