Values for which a line is a tangent

Question

The question is to "Find the values of k for which the line $y=3x$ is tangent to the cubic $y=x^3+k$". By differentiating (giving $\frac{dy}{dx}=3x^2$) I can work out that $\frac{dy}{dx}=3$ at 1 and -1... but I can't see how to work out values of k from this information. Any hints?

Answer 1

the slope of your function $$y=x^3+k$$ must be equal to the slope of the given Tangent line, this means $$3x^2=3$$

Answer 2

Use the fact that the tangent line touches the curve at 2 points, in this case, ($1,3$) and ($-1,-3$). Can you proceed now?