Solve Stationary Points: [-5, 5]

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SUMMARY

The function g(x) = x + sin(x) has two stationary points within the interval [-5, 5], specifically at x = π and x = -π. This conclusion is derived from the first derivative g'(x) = 1 + cos(x), which equals zero when cos(x) = -1. Both stationary points are confirmed to lie within the specified interval, validating the solution provided.

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[SOLVED] Stationary points

Homework Statement


Does the funtion g(x) = x + sin(x) have any stationary points on the interval [-5,5], if so where?

The Attempt at a Solution


Stationary points is where there is a 0 slope so here is what I did. Just need someone to check to see if this is right.

g'(x) = 1 + cos(x)
cos(x) = -1

So for the answer I got two stationary points at pi and -pi.
 
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Looks fine to me. Note that pi and -pi are in fact in your interval.
 
yes, thanks.
 

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