Question

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

Answer 1

First, let us evaluate the function:

`(2(x+h)^2-x+h-2x^2+x)/(h)`

Simplify:

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

Solve like terms:

`(4xh+2h^2-h)/(h)`

Factorize h from the numerator:

4xh +2h²-h = h(4x+2h-1)

Then

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