Help with a Calculus problem

[sdaccord01]

I'm helping tutor a student in Calculus right now and it's been years since I've been exposed to the subject. I was able to figure out how to do most of the sample problems, but the following one stumped me:

f(3) = 15
f(6) = 3
f'(3) = -8
f'(6) = -2

g is differentiable, and g = f^-1 (g is the inverse of f) for all x

what is g'(3)?

How do I solve this problem?

 

[chubbyfatazn]

42

 

[cubby1223]

hold on...

 

[iCyborg]

From f(6)=3 you have that g(3)=6.
Now use the formula g'(a)=1/(f'(g(a))) to get g'(3)=-1/2.

 

[cubby1223]

shouldn't it be positive 1/2

scratch that

negative 1/2

 

[halik]

-2

edit: err whops that's not for g'(x)

 

[sdaccord01]

Looks like the answer is -1/2, thanks a lot for your help!

 

[eLiu]

From f(6)=3 you have that g(3)=6.
Now use the formula g'(a)=1/(f'(g(a))) to get g'(3)=-1/2.

OP, if your friend isn't aware of where this formula comes from, it's a simple & useful exercise to derive it.

Hint: chain-rule

 

[rudder]

How do I solve this problem?

Post the problem somewhere and ask for assistance... simple really.

 

[shortylickens]

Either your semester starts late and ends late or you are REALLY far behind.

 

[NikolaeVarius]

How are you anywhere near "qualified" to tutor if its been years since you've been exposed to it?

 

[shortylickens]

How are you anywhere near "qualified" to tutor if its been years since you've been exposed to it?

Because American kids are really far behind in math and nobody wants to be a math teacher and American kids are too dumb & lazy to find lessons online and teach themselves?