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#1 2017-11-18 09:23:48
- Hannibal lecter
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- Registered: 2016-02-11
- Posts: 392
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
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- Registered: 2010-06-20
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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
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2017-11-19 09:24:52
- Hannibal lecter
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- Registered: 2016-02-11
- Posts: 392
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 .
Wisdom is a tree which grows in the heart and fruits on the tongue
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#5 2017-11-20 01:56:48
- Bob
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- Registered: 2010-06-20
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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
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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