Mathematics

Mathematics

Problem

A continuous function

h

is defined by

h(t)=\begin{cases} t & \text{for } 0 \le t \le 2,\\ 4 & \text{for } 2 < t \le 5. \end{cases}

Let

H

be an antiderivative of

h

with

H(0)=-1

. (a) Compute the exact value of

H(2)

. (b) Compute the exact value of

H(5)

. (c) For

0\le x\le 5

, at which

x

-value(s) does

H

increase most rapidly? Justify your answer.

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