Answer:
C
Step-by-step explanation:
We are given that:
[tex]\displaystyle k(x)=\frac{f(x)}{g(x)}[/tex]
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:
[tex]\displaystyle k^\prime(x)=\frac{f^\prime(x)g(x)-f(x)g^\prime(x)}{(g(x))^2}[/tex]
We want to find k’(3). Substitute:
[tex]\displaystyle k^\prime(3)=\frac{f^\prime(3)g(3)-f(3)g^\prime(3)}{(g(3))^2}[/tex]
Using the table, make the appropriate substitutions:
[tex]\displaystyle k^\prime(3)=\frac{5(2)-(-1)(-2)}{(2)^2}[/tex]
Evaluate:
[tex]\displaystyle k^\prime(3)=\frac{10-2}{4}=\frac{8}{4}=2[/tex]
Therefore, our answer is C.
