Polynomial Curve Sketching Calculus

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function g(x), g''(3)=28 indicates that g(x) is ____________ at x=3.

• increasing

• decreasing

• concave up

• concave down

When is a function concave up?

• f"(c) < 0

• f'(c) < 0

• f"(c) > 0

• f'(c) > 0

When is a function concave down?

• f"(c) < 0

• f'(c) < 0

• f"(c) > 0

• f'(c) > 0

Where do you find intervals where a function is increasing?

• f'(x) > 0

• f"(x) > 0

• f'(x ) < 0

• f"(x) < 0

What is a point of inflection?

• When a function goes from increasing to decreasing

• When a function goes from concave up to concave down

• When a function goes from decreasing to increasing

• When a function crosses the x-axis

Where are the critical numbers of a function?

• The derivative of the function equals zero

• The function has a domain restriction

• The function equals zero

• The derivative equals zero or the function does not exist

If f'(x) > 0 over the interval (-7,1), then what will be true about f(x) over this interval?

• It's constant

• It's increasing

• It's decreasing

• Cannot be determined

Given a function g(x), if g''(x) = 0 for a certain value of x, then g(x) has _________ at x.

• an inflection point

• a maximum

• a minimum

• a critical point

Given a function, f(x), if f'(x) < 0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing

• increasing

• concave up

• concave down