Question

For the function $f(x)=-3 x+4$, find and simplify
$$
\frac{f(x+h)-f(x)}{h}
$$

Answer 1

$ \textbf{Answer:}$

$-3$

$ \textbf{Explanation:}$

We are given $ f(x) = -3x+4$ which implies $ f(x+h) = -3(x+h)+4$

so,

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

$ \implies \frac{ (-3(x+h)+4) - (-3x+4)}{h}$

$ \implies \frac{ -3x-3h+4+3x-4}{h}$

$ \implies \frac{-3h}{h} $

$ \implies -3$