SOLUTION: 3. Find the equation of each tangent of the function f(x) = x3 +x2 +x+1 which is perpendicular to the line 2y + x +5=0. 3.

Algebra ->  Test -> SOLUTION: 3. Find the equation of each tangent of the function f(x) = x3 +x2 +x+1 which is perpendicular to the line 2y + x +5=0. 3.      Log On


   

Question 1034488: 3. Find the equation of each tangent of the function f(x) = x3 +x2 +x+1 which is perpendicular to the line 2y + x +5=0. 3.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E3+%2Bx%5E2+%2Bx%2B1 ==> f'(x) = 3x%5E2%2B2x%2B1.
Now the line 2y + x +5=0 has slope -1/2. Any line perpendicular to it must have slope 2.
We now find points on the graph whose tangents have slope 2.
==> f'(x) = 3x%5E2%2B2x%2B1+=+2 ==> 3x%5E2%2B2x-1+=+0
==> (3x-1)(x+1) = 0 ==> x = 1/3, x = -1.
Now f(1/3) = 40/27, and f(-1) = 0.
==> The two lines are y-40%2F27+=+2%28x-1%2F3%29 and y-0+=+2%28x%2B1%29.
Simplify these equations yourself.