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bossk171

Member

Registered: 2007-07-16

Posts: 305

Derivative of an inverse function

I graduated high school last year, and was the only one in my AP calculus class to get a 5. My old calc teacher asked me to come in and help this year's calc students. I have no formal teaching experience and I haven't done most of this stuff since I finished calc last year. I protested, he insisted and I caved.

Sure enough, first question that I did with the class I got hung up on, so here it is:

f(x) = 3x²-x and g(x) = f-¹(x)

what is g'(10)?

the book I'm working out of goes through a step by step, but it's no good, can anyone offer how they would go about it? And can anyone offer (pretty please) tips on how they'd present it to a class of calculus students?

I don't have stage fright or anything, in fact I like being in front of a large crowd, but I'm very insecure about the idea of them relying on me for help...

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Derivative of an inverse function

but f(x)=3x²-x  does not have an inverse, or?

Last edited by Kurre (2008-04-08 06:53:26)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Derivative of an inverse function

Kurre is right. Rearranging f(x) gives that:

But due to the ±, it's not well-defined.

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Why did the vector cross the road?
It wanted to be normal.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Derivative of an inverse function

The book says:

If

then:

(can anyone show how that conclusion is reached?)

then the book says:

f'(x) = 6x-1

(obviously)

then:

y = 10 = 3x²-x

(not sure why I'm doing this)

and we get x = 2 (it says not to worry about the more difficult answer of x = -5/3)

From there we can get g'(10) = 1/11

(I pointed out the steps I'm hung up on above, can anyone push me along?)

THANKS

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Derivative of an inverse function

Ok, I'm pretty sure I have it:

We're told f-¹(x) = g(x)

and we know

f(f-¹(x)) = x

(by the definition of an inverse function) thus

f(g(x)) = x

the derivative (using the chain rule) is:

f'(g(x))(g'(x)) = 1

thus:

g'(x) = 1/f'(g(x))

And I think I can take it from there...

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.