Question

determine f(2). enter your answer as an exact value. f(x)=\frac{2x}{g(x)}, g(2)=3, g(2)=4

Explanation:

Step1: Apply quotient - rule

$f(x)=\frac{2x}{g(x)}$, so $f'(x)=\frac{2g(x)-2xg'(x)}{(g(x))^{2}}$

Step2: Substitute $x = 2$

$f'(2)=\frac{2g(2)-2\times2g'(2)}{(g(2))^{2}}=\frac{2\times3 - 4\times4}{3^{2}}$

Step3: Calculate the value

$f'(2)=\frac{6 - 16}{9}=-\frac{10}{9}$

Answer:

$-\frac{10}{9}$