Question

Please help calculus question urgent

Answer 1

C

Explanation:

We are given that:

`\displaystyle k(x)=(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)=(f^\prime(x)g(x)-f(x)g^\prime(x))/((g(x))^2)`

We want to find k’(3). Substitute:

`\displaystyle k^\prime(3)=(f^\prime(3)g(3)-f(3)g^\prime(3))/((g(3))^2)`

Using the table, make the appropriate substitutions:

`\displaystyle k^\prime(3)=(5(2)-(-1)(-2))/((2)^2)`

Evaluate:

`\displaystyle k^\prime(3)=(10-2)/(4)=(8)/(4)=2`

Therefore, our answer is C.