sketch graph of function

Question

Sketch a possible graph of a function that satisfies the given conditions. (0)=−2,(2)=4
′(2)=0,′(1) is not defined ′()<0 on (−∞,1) and (2,∞) ′′()>0 on (−∞,1) ′′()<0 on (1,∞)

Answer 1

Lets try and write examine these special conditions. Firstly

Look at gradients. It is negative everywhere except on[1,2] and 0 at 2.

Then we see that if it isnt a line what kind of convex it will be. We use the 2nd derivative to find this. Finally we move the graphs till they satisfy the conditions, also, but having a discontinuity at 1, prevents f '(x) being defined there

Click here to see a graph which satisfies the conditions you stated. I leave it to you to check them.