### Home > APCALC > Chapter 4 > Lesson 4.1.3 > Problem4-34

4-34.
1. Write the equations of the two lines tangent to the curve $f\left(x\right) = x^{3} – x^{2} + x + 1$ that have a slope of $2$.

Set slope function equal to $2$: $f^\prime\left(x\right) = 2$ and solve for $x$. You should get two solutions.

Evaluate $f\left(x\right)$ 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.

2. Determine the equations of the lines perpendicular to the tangent lines from part (a) at their points of tangency to $f$.

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