Let f(x) = x|x|. (a) Sketch the graph of the function. 2 y У 4 2 2 y 4 2 y X y X J -4 -2 -2 2 -4 -2 -2 x 2 -4 -2 -2 -4 -4 -2 -2 2 (b) For what values of x is f differentiable? Ox<0 ○ x = 0 all real x (c) Find a formula for f'. f'(x) =

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.