Definition of deriviative, factoring problem

1. Oct 18, 2007

gabby989062

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?
:rofl::zzz:

Last edited: Oct 18, 2007
2. Oct 18, 2007

atqamar

Simplify the numerator, and try factoring first two terms, and then the next two terms.

3. Oct 18, 2007

HallsofIvy

Staff Emeritus
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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