Survey of Calc: Differences in f(x), f'(x), and f''(x)

This is my personal study set for MATH 121 at USD from Greywall. I recommend studying shuffled and definition review only.

If f(x) is concave up, then f’(x) is _____.

increasing

If f(x) is concave down, then f’(x) _____.

decreasing

If f(x) is concave up, then f’’(x) _____.

f’’(x) > 0

If f(x) is concave down, then f’’(x) _____.

f’’(x) < 0

If f’(x) is increasing, then f(x) _____.

concave up

If f’(x) is decreasing, then f(x) _____.

concave down

If f’(x) is increasing, then f’’(x) _____.

f’’(x) > 0

If f’(x) is decreasing, then f’’(x) _____.

f’’(x) < 0

If f’’(x) > 0, then f(x) _____.

concave up

If f’’(x) < 0, then f(x) _____.

concave down

If f’’(x) > 0, then f’(x) _____.

increasing

If f’’(x) < 0, then f’(x) _____.

decreasing

If f(x) is an inflection point, then f’(x) ____.

a local max or min

If f’(x) is a local max, then f(x) ___.

inflection point

If f’(x) is a local min, then f(x) ___.

inflection point

If f’(x) is a local max, then f’’(x) ___.

changes from (+) to (-)

If f’(x) is a local min, then f’’(x) ___.

changes from (-) to (+)

If f’’(x) changes from (+) to (-), then f’(x) ___.

local max

If f’’(x) changes from (-) to (+), then f’(x) ___.

local min

If f(x) is increasing, then f’(x) ____.

positive

If f(x) is decreasing, then f’(x) ____.

negative

If f’(x) is positive, then f(x) ____.

increasing

If f’(x) is negative, then f(x) ____.

decreasing

If f(x) is a local max, the f’(x) ___.

changes from (+) to (-)

If f(x) is a local min, the f’(x) ___.

changes from (-) to (+)

If f’(x) changes from (+) to (-), then f(x) ____.

local max

If f’(x) changes from (-) to (+), then f(x) ____.

local min