Concavity and The Second Derivative Test CW

The concavity of a function is described by its _______________. #1

• first derivative
• second derivative
• third derivative
• expression

What will be true at an inflection point?  (select the best answer) #2

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

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

• increasing
• decreasing
• concave up
• concave down

If f''(x)>0, then what will be true about f'(x) over that same interval? #4

• f '(x) is constant

• f '(x) is increasing

• f '(x) is decreasing

• f '(x) must have an inflection point in that interval

f(x) is pictured. Inflection points are most likely at which x values? #5

• x=0 and 1.5

• x=2 and 2.5

• x=2.25

• x=1

Which of the following describes an interval of f(x) that is both decreasing and concave up? #6

• f '(x) < 0 and f "(x) < 0

• f '(x) < 0 and f "(x) > 0

• f '(x) > 0 and f "(x) > 0

• f '(x) > 0 and f "(x) < 0

Find the second derivative of the function: #7
f (x) =  2x - 5x⁶

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

Match the following. #8

• the 2nd derivative to determine if a critical point is a local extrema and if so what type.

• Critical points are...

• where the 1st derivative equals 0 or is undefined.

• The 2nd Derivative Test uses...

• finding the area under a curve.

• Finding a derivative means...

• finding the slope of a tangent line.

• Evaluating an integral means...

• the first derivative to determine if a critical point is a local extrema and if so what type.

• The 1st Derivative Test uses...