# Find and simplify the different quotient f(x+h)-f(x) / h f(x)=-x^2+5x+5 f(x+h)-f(x) / h =????

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parjzna12512

Mathematics

### Question Description

Find and simplify the different quotient f(x+h)-f(x) / h

f(x)=-x^2+5x+5

f(x+h)-f(x) / h =????

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## Explanation & Answer

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$f(x)=-x^2+5x+5\\ \\ f(x+h)=-(x+h)^2+5(x+h)+5\\ \\ f(x+h)=-(x^2+2xh+h^2)+5x+5h+5\\ \\ f(x+h)=-x^2-2xh-h^2+5x+5h+5\\ \\ f(x+h)-f(x)=-x^2-2xh-h^2+5x+5h+5-(-x^2+5x+5)\\ \\ f(x+h)-f(x)=-x^2-2xh-h^2+5x+5h+5+x^2-5x-5\\ \\ f(x+h)-f(x)=-2xh-h^2+5h\\ \\$

Difference quotient is

$\frac{f(x+h)-f(x)}{h}=\frac{-2xh-h^2+5h}{h}\\ \\ \frac{f(x+h)-f(x)}{h}=\frac{h(-2x-h+5)}{h}\\ \\ \frac{f(x+h)-f(x)}{h}=-2x-h+5\\$

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fulnzanve3 (279)
Carnegie Mellon University
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