CPM Homework Help : APCALC Problem 4-34

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 $2$ .
Step 1(a):
Set slope function equal to $2$ : $f^\prime\left(x\right) = 2$ and solve for $x$ . You should get two solutions.
Step 2(a):
Evaluate $f\left(x\right)$ at both values of $x$ . This will give you the two points of tangency.
Step 3(a):
Write the equation of the two tangent lines in point-slope form.
Determine the equations of the lines perpendicular to the tangent lines from part (a) at their points of tangency to $f$ .
Hint (b):
Perpendicular lines have negative reciprocal slopes.

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