Define the function by .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Define the function

h: \mathbb R\to\mathbb R

h(x)=x|x|-6x

. (a) Express

h(x)

explicitly as a piecewise function without the absolute value symbol. (b) Identify all critical points of

h

, including points where

h

is not differentiable. (c) Find the intervals on which

h

is increasing and those on which it is decreasing. (d) State the coordinates of each local extremum of

h

, if any exist.