Calc Quick Curve Sketching Mini-Practice

a) If f'(x) = 0 and f''(x) < 0, then f(x) is.. (a)  

b) If f'(x) = 0 and f''(x) > 0, then f(x) is...​ (b)  

c)If f'(x) = 0 and f''(x) = 0, then f(x) is...​ (c)  

• an absolute minimum at that point

• an absolute maximum at that point
• a relative maximum at that point
• a relative minimum at that point
• has great concavity
• a point of inflection

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

• increasing
• decreasing
• concave up
• concave down

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Which graph is the derivative of the top graph?

• A
• B
• C
• D

Select all the local extrema (critical points)

Select all the points of inflection

Select all the points of inflection

What is the significance of a zero second derivative at a point where the first derivative is also zero?

• It indicates a local maximum and minimum together.

• It suggests a potential inflection point, but further analysis is needed to confirm if there is a change in concavity

• It means the function is constant at that point.