Question

Review Photo Please Solve in a timely manner. Lost connection with previous tutor steps understood.

Answer 1

Given the expression

$f(x)=4x^2-8$

Then

$f(x+h)=4(x+h)^2-8$

The next step is to substitute the values into the expression

$\frac{f(x+h)-f(x)}{h}=\frac{4(x+h)^2-8-(4x^2-8)}{h}$

=>

$\frac{4x^2+8xh+h^2-8-4x^2+8}{h}=\frac{h^2+8xh}{h}$

=>

$\frac{h(h+8x)}{h}$

=>

$\begin{gathered} h+8x \\ If\text{ we take the limit as h tends to 0} \\ \Rightarrow0+8x \\ \\ \Rightarrow8x \end{gathered}$

Answer = 8x