Question

Evaluate [f(x+h)-f(x)]/h if (x^2) -2x

Answer 1

\[\large f(x)=x^2-2x\]


\[\large f(x+h)=(x+h)^2-2(x+h)\]


\[\large f(x+h)=x^2+2xh+h^2-2x-2h\]
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\[\large \frac{f(x+h)-f(x)}{h}\]


\[\large \frac{(x^2+2xh+h^2-2x-2h)-(x^2-2x)}{h}\]


\[\large \frac{x^2+2xh+h^2-2x-2h-x^2+2x}{h}\]


\[\large \frac{2xh+h^2-2h}{h}\]


\[\large \frac{h(2x+h-2)}{h}\]


\[\large 2x+h-2\]


\[\large 2x-2+h\]
So \[\large \frac{f(x+h)-f(x)}{h}=2x-2+h\]

Answer 2

Thanks a bunch Bro! WWWYKI