Question

find $g(4)$ given that $f(4)= - 3$, $f(4)=4$, and $g(x)=\frac{2x + 9}{f(x)}$. $g(4)=$

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $g(x)=\frac{u(x)}{v(x)}$, then $g^{\prime}(x)=\frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v^{2}(x)}$. Here, $u(x)=2x + 9$ and $v(x)=f(x)$. So, $u^{\prime}(x)=2$ and $v^{\prime}(x)=f^{\prime}(x)$. Then $g^{\prime}(x)=\frac{2\cdot f(x)-(2x + 9)\cdot f^{\prime}(x)}{f^{2}(x)}$.

Step2: Substitute $x = 4$

We know that $f(4)=-3$ and $f^{\prime}(4)=4$. Substitute these values into the formula for $g^{\prime}(x)$:

$$
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$$

Answer:

$-\frac{74}{9}$