Question

The curve y=2x^3-3x^2-36x+15 has a turning point at (3, -66) and (-2,59). Identify whether each of these points is a maximum or a minimum. (show all your work).

Answer 1

Given curve-

y=2x^3-3x^2-36x+15

Differentiating y w.r.t. x-

$y'=6x^2-6x-36~~~~~-(1)$

Again differentiating it w.r.t x-

$y''=12x-6$

Putting x=3, $y''=12(3)-6=30>0$

Since y''>0, Point (3,-66) is a minimum points.

Now Putting x=-2, $y''=12(-2)-6=-30<0$

As y''<0, So Point (-2,59) is local maximum.