f, f', f''

If f(x) is concave down everywhere, then -f(x) is

Concave up

f''(x) is positive if f(x) is

Concave up

If f(x) has an inflection point, then f(x) has a change in

Convaity

If f(x) is concave down, then f'(x) is

Decreasing

f''(x) is negative if f'(x) is

Decreasing

f'(x) is negative if f(x) is

Decreasing

If f'(x)=0 for all values of x, then f(x) is a

Horizontal line

If f'(a)=0, then f(x) has a

Horizontal tangent line at x=a

If f(x) is an exponential decay curve, then f'(x) is

Negative and increasing

If f'(x) is increasing, then f''(x) is

Positive

If f(x) is increasing, then f'(x) is

Positive

If f(x) has a corner at x=a, then f'(a) is

Undefined

If f(x) has a horizontal tangent, then f'(x) has a

Zero

If f'(x) is decreasing, then f(x) is

Concave down

If f'(a)=2 and g(x) = f(x)-5, then g'(a)=

f'(a)=2

If f'(x) > 0 and f''(x) < 0, then f(x) looks

Increasing and concave down

If f''(x)=0 for all values of x, then f(x) is

Linear

If f'(x) has a change in sign and is always defined, then f(x) has either a

Local maximum or minimum