If and (f*g) ' (1) = 6 and g' (1) = - 1, then g (1) =

A. 5

B. - 7

C. 7

D. 5

E. 8

(note: (f*g) ' (1) means the derivitive of f (x) g (x) at x=1)

wow, the answer is 5, but why?

ples show all work and logic (don't just refernce to an online solver)

I think, the answer will be - 7

We have:

f (x) = 1 / (x-2)

g (x)

Then:

(fg) (x) = [1 / (x-2) ] (g (x)) = g (x) / (x-2)

Now; we calculate: (fg) ' (x)

Remember: (u/v) = (u'v-vu') / v²

Therefore:

(fg) ' (x) = [g' (x) * (x-2) - 1*g (x) ] / (x-2) ²

We know that:

g' (1) = - 1

(fg) ' (1) = 6

Therefore:

6=[-1 * (1-2) - g (1) ] / (1-2) ²

6=[1-g (1) ]/1

6=1-g (1)

-g (1) = 6-1

g (1) = - 5

Answer: B. - 5