How do I find the x values at which the tangents to the graphs f(x)=2x^2 and g(x)=x^3 have the same slope?

Answer 1

f'(x) = 4 x
g'(x) = 3 x^2
when does 4x = 3 x^2 ?
3 x^2 - 4 x = 0
x (3x -4) = 0
x = 0 and x = 4/3

Answer 2

Assuming you are looking for the same value of x at which both tangents are parallel.

Take derivative of each, equate and solve for x.

f'(x)=4x
g'(x)=3x²
Equate and solve to get
x=0 or x=4/3

See:
http://img855.imageshack.us/i/1299374046.png/