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Write the equations of the lines tangent to the curve at both and . 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 or .

Find the points by evaluating the original function at or .

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