Question

Hello, I need assistance with this question. Thank you so much! :) Let ()=2^2−+5. Find (+ℎ) −() / ℎ.

Answer 1

The function is given as,

$f(x)=2x^2-x+5$

It is asked to find the value of the expression,

$\frac{f(x+h)-f(x)}{h}$

Substitute the values and simplify,

$\begin{gathered} =\frac{\mleft\lbrace2(x+h)^2-(x+h)+5\mright\rbrace-(2x^2-x+5)}{h} \\ =\frac{2(x+h)^2-x-h+5-2x^2+x-5}{h} \\ =\frac{2(x^2+2xh+h^2)^{}-h-2x^2}{h} \end{gathered}$

Simplify the expression further,

$\begin{gathered} =\frac{2x^2+4xh+2h^2^{}-h-2x^2}{h} \\ =\frac{4xh+2h^2-h}{h} \\ =\frac{h(4x+2h^{}-1)}{h} \\ =4x+2h^{}-1 \end{gathered}$

Thus, the value of the required expression is,

$\frac{f(x+h)-f(x)}{h}=4x+2h-1$