Question

Difference quotient

Answer 1

`f(x)=5x^2-5x-6 \\ \quad \\ \begin{cases} f(\boxed{x+h})=5(\boxed{x+h})^2-5(\boxed{x+h})-6 \end{cases}\qquad thus \\ \quad \\ \cfrac{f(x+h)-f(x)}{h}\qquad \textit{will be then} \\ \quad \\ \cfrac{[5({x+h})^2-5({x+h})-6]\quad -\quad [5x^2-5x-6]}{h} \\ \quad \\ \cfrac{[5(x^2+2xh+h^2)-5(x+h)-6]-[5x^2-5x-6]}{h}`


`\cfrac{\underline{5x^2}+10xh+5h^2\underline{-5x}-5h\underline{-6}\underline{-5x^2}\underline{+5x}\underline{+6}}{h}\impliedby \textit{canceling those ones} \\ \quad \\ \cfrac{10xh+5h^2-5h}{h}\impliedby \textit{common factor} \\ \quad \\ \cfrac{5\underline{h}(2x+h-1)}{\underline{h}}`

and surely, you'd know what that is