Question

If M(x)=2f(x)/g(x), what is the value of M'(-1)?
We have to use the quotient rule, and there's a table. I'll try to write what's needed to do the problem.
f(x) when x=-1 is 3, f'(x) when x=-1 is -2, g(x) when x=-1 is 1, and g'(x) when x=-1 is also 1.
Please show steps!
I got M'(-1)=-10, but I'm unsure.
Thanks!

Answer 1

You need to apply quotient rule for the f/g part.

Answer 2

recall \[(\frac{f(x)}{g(x)})'=\frac{f'(x) \cdot g(x)-f(x) \cdot g'(x)}{(g(x))^2}\]

Answer 3

now just multiply 2 on both sides to get (2f/g)'

Answer 4

and since you are asked to find M'(-1)
replace the x's with -1

Answer 5

then use f(-1)=3
f'(-1)=-2
g(-1)=1
and g'(-1)=1

Answer 6

then use order of operations to simiplify