From f' to f

In this activity you will play detective, deducing information about a function f(x), the graph of whose derivative f '(x) is depicted above.

(1)(a) On which intervals is f(x) increasing?
(b) How do you know?




(c) On which intervals is f(x) decreasing?
(d) How do you know?





(2)(a) On which intervals is f(x) concave up?
(b) How do you know?




(c) On which intervals is f(x) concave down?
(d) How do you know?


(e) List the inflection points of f(x)
(f) Why are these inflection points?




(3)(a) Where does f(x) have a local max?
(b) How do you know?




(c) Where does f(x) have a local min?
(d) How do you know?




(4) Suppose we also know that f(0)=0. Give a sketch the graph of f(x) on the same axes as where f '(x) is drawn.



























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