How to find the maximum and minimum when given derivative?

enter image source here Can someone please explain where I went wrong with 4g? I got max at -3 and min at 4 by drawing the sign graph, but the answer says the exact opposite.
Thanks!

1 Answer
Oct 3, 2017

We start by finding critical numbers:

0 = -x^2 + x + 12

0 = x^2 - x - 12

0 = (x - 4)(x + 3)

x = 4 or -3

So you are correct about the two turning points.

If we select a test point between the two turning points, say x = 0 we get:

y' = 0^2 + 0 + 12 = 12

Since this is positive we know that the function is increasing on (-3, 4). Then the function is decreasing on (4, oo) and thus x = 4 will be a maximum and x = -3 will be a minimum.

Hopefully this helps!