Question

For the functions f(x)= 2x ^2 -x , evaluate and simplify equation below

Answer 1

First, let us evaluate the function:

$\frac{2(x+h)^2-x+h-2x^2+x}{h}$

Simplify:

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

Solve like terms:

$\frac{4xh+2h^2-h}{h}$

Factorize h from the numerator:

4xh +2h²-h = h(4x+2h-1)

Then

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