### Home > CALC > Chapter 3 > Lesson 3.4.2 > Problem3-161

3-161.

Find the equations of the lines tangent to the curve $y = x^3 − 4x$ at both $x = 0$ and $x = 2$. Then, determine the point of intersection for these two tangent lines.

To find the equation of a tangent line:

Find the slope by evaluating the derivative function at $x = 0$ or $x = 2$.

Find the points by evaluating the original function at $x = 0$ or $x = 2$.

Write each equation using point-slope form.

To find the point of intersection:

Using the two tangent lines, write and solve a system of equations.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Calc 3-161 HW eTool