Question

use the four - step process to find f(x) and then find f(-1), f(3), and f(9).
f(x)=2x^{2}+x - 1
f(x)=
f(-1)= (type an integer or a simplified fraction.)
f(3)= (type an integer or a simplified fraction.)
f(9)= (type an integer or a simplified fraction.)

Explanation:

Step1: Find f(x + h)

$$
LATEXBLOCK0
$$

Step2: Find f(x + h)-f(x)

$$
LATEXBLOCK1
$$

Step3: Find $\frac{f(x + h)-f(x)}{h}$

$$
LATEXBLOCK2
$$

Step4: Find $\lim_{h

ightarrow0}\frac{f(x + h)-f(x)}{h}$

$$
LATEXBLOCK3
$$

Now find $f^{\prime}(-1), f^{\prime}(3), f^{\prime}(9)$:

• When $x=-1$, $f^{\prime}(-1)=4\times(-1)+1=-3$
• When $x = 3$, $f^{\prime}(3)=4\times3+1=13$
• When $x = 9$, $f^{\prime}(9)=4\times9+1=37$

Answer:

$f^{\prime}(x)=4x + 1$
$f^{\prime}(-1)=-3$
$f^{\prime}(3)=13$
$f^{\prime}(9)=37$