Calculus

John · 2005-09-24 13:09:05

Find the derivative of the function:
f(x) = [(x^3) - 3(x^2) + 4]/x^2

This is an odd-numbered problem, so I checked my answer on the back of the book--which was wrong--and the answer it gave was: [(x^3)-8]/x^3.

Please help me understand this problem...how did the book come up with that answer? Any help would be much appreciated. Thanks in advance.

Atled · 2005-09-24 13:27:23

f(x)= [(x^3) - 3(x^2) + 4]/x^2

divide through by x^2

you get

f(x) = x - 3 + 4x^(-2)

use the power rule f(x) = x^n f'(x) = n*x(n-1)

f'(x) = 1 - 8*x^(-3)

then factor out x^(-3)

[x^3 - 8]*x^(-3) = [(x^3)-8]/x^3

John · 2005-09-24 13:45:14

That helped me so much. I can't believe I missed the simple process of factoring out the x^-3
Thanks again.

John E. Franklin · 2007-03-01 16:55:51

I double checked this his way, or with quotient rule, and it is right!!!
Diggin' up old material.

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