# The Fundamental Theorem of Calculus

### Exercises

#### Exercise 7

A cat climbs up and down a tree with velocity given by the graph below. When the velocity is positive it means the cat is climbing up the tree.

(a) At what time(s) does the cat change direction?

(b) At what time(s) is the cat climbing most rapidly upwards?

(c) At what time(s) is the cat climbing most rapidly downwards?

(d) What is the cat's fastest speed on the interval [0,7]?

(e) What is the cat's slowest speed on the interval [0,7]?

(f) At what time(s) is the cat highest in the tree?

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