Thread: Interesting Question

This is from a Mu Alpha Theta Competition I took today.

19. Let f and g be functions such that . What is ?

A) Not enough information
B)2
C)
D)8x-2


I didn't really know how to approach this, so a little push would be great.

Originally Posted by Jameson

This is from a Mu Alpha Theta Competition I took today.

19. Let f and g be functions such that . What is ?

A) Not enough information
B)2
C)
D)8x-2


I didn't really know how to approach this, so a little push would be great.

Rewrite as:



Now differentiate wrt x.

RonL

Originally Posted by CaptainBlack

Rewrite as:



Now differentiate wrt x.

RonL

How do you know it is differenciable

Originally Posted by ThePerfectHacker

How do you know it is differenciable

1. It is a linear form in and so differentiable wrt .

2. If and are differentiable then this is differentiable. Asking the
question implies we may assume that and are differentiable, just
as it allows us to assume that denotes the derivative.


RonL

I was making a remark that in analysis you always need to show diffrenciability before taking the derivative, I just found that funny.

Originally Posted by CaptainBlack

Rewrite as:



Now differentiate wrt x.

RonL

So I get that , so my answer is 2.

Originally Posted by Jameson

So I get that , so my answer is 2.

That's what I get

RonL