A function has derivative given by for all real

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

A function

h

has derivative given by

h'(x)=|2x-1|

for all real

x

. The value of the function at the origin is

h(0)=-3

. (a) Write

h'(x)

as a piecewise-defined function without the absolute-value symbol. (b) Obtain a piecewise formula for

h(x)

that satisfies the given initial condition. (c) Evaluate

h(2)