cpcalc 4.2.3

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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

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

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  $f\left(x\right)=x^3+6x^2$  ?

•  $x=0$  

•  $x=-4$  

•  $x=-2$  

•  $x=2$  

What is a point of inflection?

• When a function goes from increasing to decreasing.

• When the concavity changes.

• When the derivative changes.

• When the function crosses the x-axis.

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

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