### Home > CALC > Chapter 4 > Lesson 4.1.3 > Problem 4-34

4-34.

Complete the following. Homework Help ✎

Find the equations of the two lines tangent to the curve

*f*(*x*) =*x*^{3}−*x*^{2}+*x*+ 1 that have a slope of 2.Determine the equations of the lines perpendicular to the tangent lines from part (a) at their points of tangency to the graph.

Set slope function equal to 2: *f* '(*x*) = 2 and solve for *x*. You should get two solutions.

Evaluate *f*(*x*) at both values of *x*. This will give you the two points of tangency.

Write the equation of the two tangent lines in point-slope form.

Perpendicular lines have negative reciprocal slopes.

Use the eTool below to examine the graph.

Click the link at right for the full version of the eTool: Calc 4-34 HW eTool