Question

Please help calculus question urgent

Answer 1

Answer:

C

Step-by-step explanation:

We are given that:

$\displaystyle k(x)=\frac{f(x)}{g(x)}$

And we want to find k'(3).

So, let's find k'(x). Take the derivative of both sides. This will require the Quotient Rule. Hence:

$\displaystyle k^\prime(x)=\frac{f^\prime(x)g(x)-f(x)g^\prime(x)}{(g(x))^2}$

We want to find k’(3). Substitute:

$\displaystyle k^\prime(3)=\frac{f^\prime(3)g(3)-f(3)g^\prime(3)}{(g(3))^2}$

Using the table, make the appropriate substitutions:

$\displaystyle k^\prime(3)=\frac{5(2)-(-1)(-2)}{(2)^2}$

Evaluate:

$\displaystyle k^\prime(3)=\frac{10-2}{4}=\frac{8}{4}=2$

Therefore, our answer is C.