Question

use the given information to find ( f(2) ).
( g(2) = 4 ) and ( g(2) = -2 )
( h(2) = -1 ) and ( h(2) = 3 )
( f(x) = \frac{g(x)}{h(x)} )
( f(2) = )

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1. 0 / 0.2 points

use the given information to find ( f(3) ).
( f(x) = g(x)h(x) )
( g(3) = -8 ) and ( g(3) = -2 )
( h(3) = -6 ) and ( h(3) = 6 )
( f(3) = )

Explanation:

Step1: Apply Quotient Rule to $f(x)$

For $f(x)=\frac{g(x)}{h(x)}$, $f'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}$

Step2: Substitute $x=2$ values

Substitute $g(2)=4$, $g'(2)=-2$, $h(2)=-1$, $h'(2)=3$:
$f'(2)=\frac{(-2)(-1)-(4)(3)}{(-1)^2}$

Step3: Calculate numerator and denominator

Numerator: $2 - 12 = -10$; Denominator: $1$
$f'(2)=\frac{-10}{1}=-10$

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Step1: Apply Product Rule to $f(x)$

For $f(x)=g(x)h(x)$, $f'(x)=g'(x)h(x)+g(x)h'(x)$

Step2: Substitute $x=3$ values

Substitute $g(3)=-8$, $g'(3)=-2$, $h(3)=-6$, $h'(3)=6$:
$f'(3)=(-2)(-6)+(-8)(6)$

Step3: Calculate each term and sum

First term: $12$; Second term: $-48$
$f'(3)=12-48=-36$

Answer:

$f'(2) = -10$
$f'(3) = -36$