SOLUTION: Given f(x)=-2x2^-5x+5, find f(x+h)-f(x)/h, h not equal to 0

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Question 1056265: Given f(x)=-2x2^-5x+5, find f(x+h)-f(x)/h, h not equal to 0
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
[f(x+h) - f(x)]/h = [-2x^2 - 4xh - 2h^2 - 5x - 5h + 5 - (-2x^2 - 5x + 5)]/h
Some of the terms in the numerator cancel and we are left with:
[f(x+h)-f(x)]/h = (-4xh - 2h^2 - 5h)/h = -4x - 2h - 5
For h very small, the middle term drops out and we are left with -4x - 5