Sketching Graphs with derivatives

Question

Sketch the graph of a function with the given characteristics:

f(2)=f(4)=0

f'(x)<0 for x<3

f'(3) does not exist

f'(x)>0 for x>3

f''(x)<0, x≠ 3

Answer 1

If you make an outline of the sketch first, it's a lot less daunting to fit it all in. Here's just one approach. As Frank pointed out, there are multiple answers.

Answer 2

See the videa.