Expert: Paul Klarreich - 11/8/2008

Question
I know this is prob a very simple question but can you help, for the life of me I cannot remember how to do calculus and my son needs help. can you tell me how do you find the equation of the tangent to the curve y = x^4 + 5x + 1 at the point where x=2

Answer
Questioner:   Kennith Simpson
Category:  Calculus
Private:  No
 
Subject:  Calculus
Question:  I know this is prob a very simple question but can you help, for the life of me I cannot remember how to do calculus and my son needs help. can you tell me how do you find the equation of the tangent to the curve y = x^4 + 5x + 1 at the point where x=2
.........................
Hi, Kennith,

This is a standard Application of Derivative (see note below.)

1. Find  dy/dx.
2. Evaluate it at x = x0  (here x0 = 2)  This is your m.
3. Find  y0 at x = x0.  (here subst  x = 2 and find y.)
4. Use the point-slope form:

  y - y0 = m(x - x0)

and you have it.

AND, Please check the archives for other examples.  There are many of them.  Click BROWSE PAST ANSWERS and look for the subject line Applications of Derivatives.