Applications of trig (1 Viewer)

kyokaku92 · May 25, 2010

Hi! I was wondering if anyone could help me solve this question

a) y = x - sinx
Find stationary points and determine their nature

b) Find pt of inflexion

c) Sketch the graph between 0

x

thanks

jet · May 25, 2010

$y = x - \sin x \\ \therefore \frac{dy}{dx} = 1 - \cos x = 0 \text{ for stationary points} \\ \therefore \cos x = 1 \Rightarrow x = 0 \text{ in the domain } 0 \leq x \leq \pi \\ \text{Either using the first or second derivatives, you can conclude that this is a horizontal point of inflexion}$

Carrotsticks · May 25, 2010

Since you know that 1-cosx cannot be negative (since the maximum value of cos is 1), it must be monotonic increasing. Just thought I should add that to the above post.

NewiJapper · May 25, 2010

shouldnt the x-axis be in pi if the domain is in pi?

ibbi00 · May 25, 2010

Yes, it should.

jet · May 25, 2010

a) It doesn't matter what the x-axis is in since pi is just 3.14
b) I plotted that on Maple and just saved it as it was, maple doesn't really care what I think.

Applications of trig (1 Viewer)

kyokaku92

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jet

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ibbi00

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jet

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