AP Calc Unit 6

f is increasing on the interval (a,b)

f’ > 0 on interval (a,b)

f is decreasing on the interval (a,b)

f’ < 0 on interval (a,b)

f has a critical point at x = a

f’(a) = 0 or undefinded

f has a relative minimum at x = a

f’ changes from negative to positive at x = a

f has a relative maximum at x = a

f’ changes from positive to negative at x = a

f is concave up on the interval (a,b)

f’’ > 0 on interval (a,b)

f is concave down on the interval (a,b)

f’’ < 0 on interval (a,b)

f has an inflection point at x = a

f’’ (a) = 0 or undefined and f’’ changes sign

Intermediate value theorem

f is continuous on [a,b] and f(a) <= k <= f(b)

Mean value theorem

f is continuous on [a,b], differentiable on (a,b) and the average rate of change of f is equal to f’(x)