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# maths question

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Suppose that a one-to-one function f has tangent line y = 5x+ 3 at the point (1, 8). Evaluate (f^{-1})'(8)

Oct 16, 2015

#3
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I thought this was interesting too.  I'd like to make it both simpler (1. below) and more complicated (2. below)! .

Oct 18, 2015

#1
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$$\mbox{what do you know about the relationship between }f^\prime(x) \mbox{ and }(f^{-1})^\prime(x) ?$$

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Oct 16, 2015
#2
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Rom, I hope that you do not mind me butting in but i could not answer your questions straight off and I wanted to think about what was happening myself.

So whether or not you are teaching the question asker, you are teaching me:)

I developed a formula for a curve that met the given criterion.

This is what I came up with.

https://www.desmos.com/calculator/7uhpqmscci I/You did not need to do any of this to answer the question, I was just thinking laterally. :)

Oct 17, 2015
edited by Melody  Oct 17, 2015
#3
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I thought this was interesting too.  I'd like to make it both simpler (1. below) and more complicated (2. below)! .

Alan Oct 18, 2015
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Thanks Alan,

In response to 1).

Yes of course I could have LOL

BUT

The graph would not hve looked as interesting In response to 2)

That makes my head hurt. Maybe I will think about it later after something deadens the pain.   LOL   again Oct 18, 2015
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1. You are right Melody, the graph would have been really boring!

2. Here are a couple of graphs to illustrate the solution when n = 2 (so f(x) = x5 + 7) .

Oct 18, 2015
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Thanks Alan,  I still like my graph.   Oct 18, 2015
edited by Melody  Oct 18, 2015
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all very nice work but you all seemed to have missed the point

$$\left(f^{-1}\right)^\prime(x)=\dfrac 1 {f^\prime(f^{-1}(x))}$$

$$\mbox{So as }f \mbox{ has a tangent line }y=5x+3, @(1,8) \\ {f^{-1}}^\prime(8) = \dfrac 1 {f^\prime(1)}=\dfrac 1 {5(1)+3}=\dfrac 1 8$$

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Oct 20, 2015