Alan G. answered • 07/12/16
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Alex,
This fraction is called the difference quotient and is extremely important in first-semester calculus.
Here's how to simplify it for f(x) = 1/x2.
f(x+h) = (x+h)2 = x2 + 2xh + h2
f(x+h) − f(x) = x2 + 2xh + h2 − x2 = 2xh + h2
Notice the last line has a factor of h in every term. This is typical when simplifying the difference quotient correctly.
Factor out the h and divide by h, which cancels it out:
[f(x+h) - f(x)]/h = (2xh + h2)/h = h(2x + h)/h = 2x + h.
The correct answer is 2x + h.
Kenneth S.
Observe that, although the student very likely is being asked to find the differencequotient, his statement o fthe problem is incorrect, lacking the necessary grouping to make the entire difference be the numerator.
Alan should have noted this disparity and so advised the student. Then, too, he should take proper steps as outlined in Mark M's comment.
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07/13/16
Alan G.
Is not 1/x2 the same function as x-2. The problem is actually simpler if the power function is written as a fraction.
Sorry to disagree, but why did you state that the student misstated the problem? It looked fine and solvable to me.
You need not reply unless you feel it is necessary.
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07/13/16
Mark M.
07/12/16