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

3-161.

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

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