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

Guest Oct 16, 2015

#1**+5 **

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

.Rom Oct 16, 2015

#2**+5 **

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. :)

The answer is very simple.

Melody Oct 17, 2015

#3**+5 **

Best Answer

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

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Alan Oct 18, 2015

#4**0 **

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

Melody Oct 18, 2015

#5**+5 **

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) = x^{5} + 7)

.

Alan Oct 18, 2015