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Homework Help: Definition of deriviative, factoring problem

  1. Oct 18, 2007 #1
    1. The problem statement, all variables and given/known data
    use definition of derivitiave to find f'(c) EXACTLY
    x3 - 4x2 + x + 8, c=1
    2. Relevant equations
    lim x->c f(x)-f(c) / x-c

    3. The attempt at a solution

    I got as far as (x3 - 4x2 +x + 2) - 6 / x-1

    Plugging in 1 for x gives me divided by zero. The teacher's example, she factored an x-1 in the numerator and cancelled it with the denominator, but she did an easy example that only had x2, and I have x3. How do I find an x-1 in the top?
    Last edited: Oct 18, 2007
  2. jcsd
  3. Oct 18, 2007 #2
    Simplify the numerator, and try factoring first two terms, and then the next two terms.
  4. Oct 18, 2007 #3


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    Science Advisor

    By the way, it is much easier to read what you really mean if you use "^" to indicate powers: x^3- 4x^2+ x+ 2, rather than x3-4x2+x+2.

    x^3- 4x^2+ x+ 2- 6= x^3- 4x^2+ x- 4= (x-1)(?).

    Knowing that one factor must be x- 1 should make that easy- just divide x^3- 4x^2+ x- 4 by x-1. If you use "synthetic division" it's even easier.
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