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#1 2017-11-18 09:23:48

Hannibal lecter
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Registered: 2016-02-11
Posts: 156
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what is the maximum expected slope for a function?

hi, how to find maximum slope for a function like " f(x) = x - cos(x) "

can you help me with that please??


Wisdom is a tree which grows in the heart and fruits on the tongue

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#2 2017-11-18 20:18:24

bob bundy
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Registered: 2010-06-20
Posts: 8,202

Re: what is the maximum expected slope for a function?

Hi,

If you differentiate the function, you have the slope at any value of x.  So now you want to know when that is a maximum. So differentiate again and set equal to zero for stationary points.  Investigate each to see which give a maximum.

These are only local maxima so you still need to consider which is the absolute one.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2017-11-19 09:24:52

Hannibal lecter
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Registered: 2016-02-11
Posts: 156
Website

Re: what is the maximum expected slope for a function?

can you calculate it to me in details please,,

is it = 1? my textbook say , it's 1

is that right?

please calculate it to me so I'll be able to solve other questions and examples .


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#4 2017-11-19 18:52:27

zetafunc
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Registered: 2014-05-21
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Re: what is the maximum expected slope for a function?

What happens when you differentiate

?

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#5 2017-11-20 01:56:48

bob bundy
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Registered: 2010-06-20
Posts: 8,202

Re: what is the maximum expected slope for a function?

If you use http://www.mathsisfun.com/data/function-grapher-old.php

you can see the graph for yourself.

Differentiating gives 1 + sin(x)  It's worth plotting this too.  You'll see that maxima occur periodically.

Differentiating the slope function gives cos(x) and this is zero at  π/2, 3π/2, 5π/2 etc.  The first and every alternate one thereafter is a maximum.  Plugging in π/2 for the slope function gives 1 + sin(π/2) = 2.  I have zoomed in on the graph and used coordinates to get the gradient directly.  Still get 2, not 1

It would be 1 for the function  1 -  cos(x).

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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