Appleman14
4

# what is the difference quotient of $2 x^{2} -x-3$

$\frac{dy}{dx}=\frac{d}{dx}(2x^2-x-3)$ $\boxed{\boxed{\frac{dy}{dx}=4x-1}}$ I guess this expression "Difference quotient" is like Slope... other way... $lim_{h\to0}(\frac{f(x+h)-f(x)}{h})$ $lim_{h\to0}(\frac{2*(x+h)^2-(x+h)-3-(2x^2-x-3)}{h})$ $lim_{h\to0}(\frac{2*(x^2+2xh+h^2)-(x+h)-3-(2x^2-x-3)}{h})$ $lim_{h\to0}(\frac{2*x^2+4xh+2h^2-x-h-3-2x^2+x+3}{h})$ $lim_{h\to0}(\frac{2h^2+4xh-h}{h})$ simplify $lim_{h\to0}(2h+4x-1)=\boxed{\boxed{4x-1}}$ like I said...