Expert: Paul Klarreich - 1/20/2012

Question
My question:

Find the equation of the line tangent to the graph of y = x^3 + x ^2 + 2 at its point of inflection.

The answer is y = -3x +1.

I don't understand why.

Answer
Questioner:Taalib
Country:Virginia, United States
Category:Calculus
Private:No
Subject:Calculus

Question:

My question:

Find the equation of the line tangent to the graph of y = x^3 + x ^2 + 2 at its point of inflection.

The answer is y = -3x +1.

I don't understand why.
.............................................
You have to do some translating of standard phrasing:

'at' :  for what value of x?

'at its point of inflection'  -- the value of x where the second derivative is zero.  Soooooo -- you will find d2y/dx2, set that to zero, solve, and you will have an x-value, which I will call x2.

'line tangent to the graph' -- having a slope, m, that is equal to dy/dx at x2.

'Find the equation of the line' --  use the standard form:

y - y2 = m(x - x2)

and you already have  x2, m, and just need y2.  I leave it to you to find that and finish up.