Complete the following. Homework Help ✎
Find the equations of the two lines tangent to the curve f(x) = x3 − x2 + 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