Expert: Paul Klarreich - 11/30/2009

Question
Hi Paul,

I am trying to determine the points on a curve of y=(1/3)x^3 - x^2 where the equation of the tangent line is parallel to the line y=3x+2

thank you for all your help!

Answer
Questioner: Kate
Country: United States
Category: Calculus
Private: Yes
Subject: calculus -- determining points on a curve
Question: Hi Paul,

I am trying to determine the points on a curve of y=(1/3)x^3 - x^2 where the equation of the tangent line is parallel to the line y=3x+2

thank you for all your help!
........................................
You don't mean:

"the equation of the tangent line is parallel to the line y=3x+2"

An equation can't be parallel to anything.

You DO mean:

"the tangent line is parallel to the line y=3x+2"

which means:

"the SLOPE of the tangent line is the same as the slope of the line WHOSE EQUATION IS y=3x+2"

which means

"the SLOPE of the tangent line is equal to 3"

which means

"the derivative of the function is equal to 3."

I think now you will be able to handle the rest.

You seem sloppy about using the vocabulary.  That is a good way to get yourself confused.