find the turning points for the curve y=2x^3-1/2x^2-x+5. Determine the nature of the turning points.

Question

Appreciate your help

Answer 1

dy/dx = 6x^2 - x - 1
= 0 at the turning points

(3x + 1)(2x - 1) = 0
x = -1/3 or x = 1/2
sub those values into original equation to get the whole points

y'' = 12x-1
when x = -1/3, y'' is negative, so x = -1/3 will yield a maximum point
when x = 1/2 , y'' is positive, , so x = 1/2 will yield a minimum point.