Question

Find the derivative of f(x) = -2x2 + 11x at x = 9.

Answer 1

$\bf f(x)=-2x^2+11x\qquad\qquad \lim\limits_{h\to 0}\ \cfrac{f(x+h)-f(x)}{h}\\\\ -----------------------------\\\\ \cfrac{[-2(\underline{x+h})^2+11(\underline{x+h})]\quad -\quad [-2x^2+11x]}{h} \\\\\\ \cfrac{[-2(x^2+2xh+h^2)+11x+11h]\quad -\quad [-2x^2+11x]}{h} \\\\\\ \cfrac{\underline{-2x^2}-4xh-2h^2\underline{+11x}+11h\quad \underline{+2x^2}\underline{-11x}}{h}$

$\bf \cfrac{-4xh-2h^2+11h}{h}\implies \cfrac{\underline{h}(-4x-2h+11)}{\underline{h}} \\\\\\ \lim\limits_{h\to 0}\ -4x-2h+11\implies -4x-2(0)+11 \\\\\\ \left. -4x+11\cfrac{}{} \right|_{x=9}\implies -4(9)+11$