f(x)=12x^2e^2x - 14, find the x-coordinates of the turning points.

f(x)=(12x^2)(e^2x) - 14, so using the chain rule f'(x)=(24x)(e^2x) + (12x^2)(2e^2x).To find the turning points set f'(x)=0, so (24x)(e^2x) + (24x^2)(e^2x) = 0. Thus (24xe^2x)(1+x)=0. Thus x=0 or x=-1.