Question

use the four - step process to find f(x) and then find f(1), f(2), and f(3).
f(x)= - 1
f(x)=
(simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the four - step process for the derivative

The four - step process for finding the derivative of $y = f(x)$ is:

1. Find $f(x + h)$:

Since $f(x)=-1$, then $f(x + h)=-1$.

1. Find $f(x + h)-f(x)$:

$f(x + h)-f(x)=-1-(-1)=0$.

1. Find $\frac{f(x + h)-f(x)}{h}$:

$\frac{f(x + h)-f(x)}{h}=\frac{0}{h}=0$ for $h
eq0$.

1. Find $\lim_{h

ightarrow0}\frac{f(x + h)-f(x)}{h}$:
$\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}=\lim_{h
ightarrow0}0 = 0$. So $f^{\prime}(x)=0$.

Step2: Evaluate $f^{\prime}(1)$

Substitute $x = 1$ into $f^{\prime}(x)$. Since $f^{\prime}(x)=0$, then $f^{\prime}(1)=0$.

Step3: Evaluate $f^{\prime}(2)$

Substitute $x = 2$ into $f^{\prime}(x)$. Since $f^{\prime}(x)=0$, then $f^{\prime}(2)=0$.

Step4: Evaluate $f^{\prime}(3)$

Substitute $x = 3$ into $f^{\prime}(x)$. Since $f^{\prime}(x)=0$, then $f^{\prime}(3)=0$.

Answer:

$f^{\prime}(x)=0$
$f^{\prime}(1)=0$
$f^{\prime}(2)=0$
$f^{\prime}(3)=0$