Find critical numbers of  f(x) = sin x, `(0 < x < 2*pi)` . Then determine if the critical number is a local minimum, local maximum, or neither

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The x value of the critical points of f(x) = sin x lie at the solution of f'(x) = 0

f'(x) = cos x

cos x = 0

=> x =` pi/2` and x = `3*pi/2`

At x = `pi/2` , sin x = 1 and at x = `3*pi/2` , sin x = -1

In the domain `(0, 2*pi)` , the function f(x) = sin x has a maximum value of 1 and a minimum value of -1.

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