Question

If $f\left(x\right)=3x^2-2x+5$, find $\underset{x\to 0}{lim}\frac{f(x+h)(-f(x)}{h}$

• A. $6x-2$
• B. $0$
• C. $\infty$
• D. indeterminate
• E. $5$

Answer 1

The correct option is A $6x-2$

Given, $f\left(x\right)=3x^2-2x+5$
$\therefore {lim}_{x\to 0}\frac{f(x+h)-f\left(x\right)}{h}={lim}_{x\to 0}\frac{3({(x+h)}^2-x^2)-2(x+h-x)+5-5}{h}$

$={lim}_{x\to 0}\frac{3(h^2+2xh)-2h}{h}$

$={lim}_{x\to 0}\frac{3(h^2+2xh)}{h}-\frac{2h}{h}$

$=6x-2$