f, f', f''

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

Concave down

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) > 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

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

f'(a)=2