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