a) The average rate of change is given by:
b) Look for the maximum point of the parabola. This occurs at x = -b/(2a) is the parabola is f(x) =ax^2 +bx + c
Algebraically, differentiate and set the derivative equal to zero, so that the tangent line to the parabola is horizontal. This occurs only at the vertex.
c) Compute h'(x). For increasing intervals, solve h'(x) > 0. For decreasing intervals, solve h'(x) < 0.