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).