Question

For what value(s) of x does the tangent to y=2x^3-3x^2+1 have slope 12?

Answer 1

when x=2

Answer 2

and x=-1

Answer 3

Find the derivative of y, set it equal to 12 and then solve for x.

The derivative will be a quadratic so you'll be able to either factor it, or, worst case scenario, use the quadratic formula.

:)

Answer 4

slope =12=dy/dx

Answer 5

dy/dx= 6x^2-6x=12.

Answer 6

x^2-x=2 -----> x^2-x-2=0 ---> (x-2)(x+1)=0 ---> x=2 and -1