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**Hannibal lecter****Member**- Registered: 2016-02-11
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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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,278

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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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 208
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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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What happens when you differentiate

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,278

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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