Question

Calcule a derivada usando a definição;
f(x)= x²-3x+2

Answer 1

$f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ =\lim_{h \to 0} \frac{(x+h)^2-3(x+h)+2-(x^2-3x+2)}{h} \\ =\lim_{h \to 0} \frac{x^2+2xh+h^2-3x-3h+2-x^2+3x-2}{h} \\ =\lim_{h \to 0} \frac{2xh+h^2-3h}{h} \\ =\lim_{h \to 0} \frac{h(2x+h-3)}{h} \\ =\lim_{h \to 0}2x+h-3=2x-3$

Assim, f'(x)=2x-3