How do you find the critical numbers of $f (x) = x + 2 sin x$ $f(x) = x + 2sinx$ ?

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Answer 1 · 2016-11-26T16:39:59

The critical points are $x = \frac{4 π}{3} + 2 π n and \frac{2 π}{3} + 2 π n$ $x = (4pi)/3 + 2pin and (2pi)/3 + 2pin$

The derivative of the function is

$f'(x) = 1 + 2cosx$

Critical points will occur whenever the derivative equals $0$ or is undefined.

$0 = 1 + 2cosx$

$-1 = 2cosx$

$-1/2 = cosx$

$x = (4pi)/3 + 2pin and (2pi)/3 + 2pin$

Hopefully this helps!

How do you find the critical numbers of f(x) = x + 2sinxf(x)=x+2sinxf(x) = x + 2sinx?