Having some difficulty with these problems. I already have the answer to the second in the back of the book, but just can't figure out how to get there.

1) Sketch the graph of a function f such that f' > 0 for all x and the rate of change of the function is decreasing.

2) f(x) = $\displaystyle ax^3$ when x $\displaystyle <=$ 2

f(x) = $\displaystyle ax^2$ when x $\displaystyle >$ 2

Find a and b such that f is differentiable everywhere.