SOLUTION: Difference Quotient A. Given the function g(x) - x^2 - 3x + 5, find the difference quotient g(x+h) - g(x)/h. B. Given the function f(x) = -x^2 + 2x -3, find the difference

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Question 183000: Difference Quotient
A. Given the function g(x) - x^2 - 3x + 5, find the difference quotient g(x+h) - g(x)/h.

B. Given the function f(x) = -x^2 + 2x -3, find the difference quotient..

Answer by stanbon(75887) (Show Source):
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Difference Quotient
A. Given the function g(x) - x^2 - 3x + 5, find the difference quotient g(x+h) - g(x)/h.
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g(x+h) = (x+h)^2 - 3(x+h) + 5
g(x+h) = x^2 + 2hx + h^2 - 3x - 3h + 5
Now subtract g(x) from f(x+h) to get:
g(x+h)-g(x) = 2hx + h^2 - 3h
Now divide by "h":
[g(x+h)-g(x)]/h = 2x + h - 3
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B. Given the function f(x) = -x^2 + 2x -3, find the difference quotient..
f(x+h) = -(x+h)^2 + 2(x+h) - 3
f(x+h) = -(x^2 + 2hx + h^2) + 2x + 2h -3
f(x+h) = -x^2 - 2hx - h^2 + 2x + 2h - 3
Now subtract f(x) from f(x+h) to get
f(x+h)-f(x) = -2hx - h^2 + 2h
Now divide by "h"
[f(x+h)-fIx)]/h = -2x - h + 2
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Cheers,
Stan H.