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April 1, 2015

April 1, 2015

Posted by **Ann** on Monday, October 7, 2013 at 1:56am.

f(x)=3x^3−42x

Compute the difference quotient

[f(x+h)−f(x)]/h,h≠0

I checked my work like 3 times and still got [(-2x^3)+(3hx^2)+(3xh^2)+(h^3)-(42h)]/h

Is it wrong?

- Pre-Calculus -
**Steve**, Monday, October 7, 2013 at 4:00amlooks like you forgot that pesky 3 out front.

f(x+h) = 3(x+h)^3 - 42(x+h)

= 3x^3 + 9x^2h + 9xh^2 + 3h^3 - 42x - 42h

f(x) = 3x^3 - 42x

subtract to get

9x^2h + 9xh^2 + 3h^3 - 42h

now divide by h to get

9x^2 + 9xh + 3h^2 - 42

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