The fact that f'> 0 tells you the graph is increasing- draw a graph that is going up as you go to the right. "The rate of change of the function is decrasing" tells you that howfastit goes up is slowing. Draw a graph that is going up but less and less steep.

Obviously (I hope it is obvious!) both and are differentiable so the only problem is at the point x= 2.2) f(x) = when x 2

f(x) = when x 2

Find a and b such that f is differentiable everywhere.

Whatisthe derivative of at x= 2? Whatisthe derivative of at x= 2? What value of x makes those the same?