Mathematics
Appleman14
4

what is the difference quotient of [latex]2 x^{2} -x-3[/latex]

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katiebabyyy

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

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