Question

question let f(x)=8x - 10 find f(4) using the definition of a derivative. provide your answer below: f(4)=□

Explanation:

Step1: Recall derivative definition

The definition of the derivative of a function $y = f(x)$ is $f^{\prime}(x)=\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}$. So for $f(x)=8x - 10$, we first find $f(x + h)$.
$f(x + h)=8(x + h)-10=8x+8h - 10$.

Step2: Substitute into derivative formula

$\frac{f(x + h)-f(x)}{h}=\frac{(8x + 8h-10)-(8x - 10)}{h}=\frac{8x+8h - 10 - 8x + 10}{h}=\frac{8h}{h}=8$.

Step3: Find the limit

$f^{\prime}(x)=\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}=\lim_{h
ightarrow0}8 = 8$. Since the derivative $f^{\prime}(x)$ is a constant function, for any $x$ - value, including $x = 4$, $f^{\prime}(x)$ has the same value.

Answer:

$8$