Define the function h:R→R by h(x)=x∣x∣−6x.
a. (a) Express h(x) explicitly as a piecewise function without the absolute value symbol.
b. (b) Identify all critical points of h, including points where h is not differentiable.
c. (c) Find the intervals on which h is increasing and those on which it is decreasing.
d. (d) State the coordinates of each local extremum of h, if any exist.