Homework Help

Find the slope of the tangent to the curve: f(x)=x^3-x^2-x+1 at x= -2Show all work.

user profile pic

foxwit | Student, Undergraduate | Salutatorian

Posted August 18, 2012 at 10:27 PM via web

dislike 1 like

Find the slope of the tangent to the curve:

f(x)=x^3-x^2-x+1

at x= -2

Show all work.

1 Answer | Add Yours

user profile pic

mlehuzzah | Student, Graduate | (Level 1) Associate Educator

Posted August 18, 2012 at 10:32 PM (Answer #1)

dislike 1 like

The slope of the tangent line of `f(x)` at `a`  is `f'(a)`   

That is, you find the derivaive of `f` and then plug in `a`

So:

`f(x)=x^3-x^2-x+1`

`f'(x)=3x^2-2x-1`

`f'(-2) = 3(-2)^2-2(-2)-1=15`

 

So the slope of the tangent line of f at -2 is 15.

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes