Julia P.

asked • 08/21/17

evaluate The Difference Quotient For The Given Function. Simplify Your Answer. f(x)=x^3, f(a+3)-f(a)/h

evaluate The Difference Quotient For The Given Function. Simplify Your Answer. f(x)=x^3, f(a+3)-f(a)/h

Mark M.

How was my solution inadequate?
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08/21/17

Julia P.

i had just written the problem incorrectly. I don't know if that affected the answer, i have not learned this yet and the teacher just threw it at us. 
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08/21/17

Arturo O.

Is the problem stated correctly?  I suspect it is really
 
[f(a + h) - f(a)] / h.
 
This is setting you up to find f'(a) for f(x) = x3, which I think is the real intent of the problem.
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08/21/17

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Arturo O. answered • 08/21/17

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I will put an answer in the Comments box due to trouble editing in the Answer window.

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Arturo O.

[f(a + h) - f(a)]/h = [(a + h)3 - a3]/h = [(a3 + 3a2h + 3ah2 + h3) - a3]/h
 
=  (3a2h + 3ah2 + h3)/h = 3a2 + 3ah + h2
 
Now take the limit as h→0 and get
 
f'(a) = 3a2
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08/21/17

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