Find critical numbers of the function.

Question

Find the critical numbers of the function:

(sin(x))^2 + cos(x) 0 < x < 2𝜋

Thank you in advance for any guidance!

Answer 1

A number is critical if it makes the derivative of the expression equal 0. Therefore, we need to take the derivative of the expression and set it to 0.

Y= (sin(x))^2 + cos(x)

Y'= 2 sin(x) cos(x)- sin(x)

Y'=sin(x)[2cos(x)-1] = 0

sin(x)=0 or cos(x)=1/2

sin(x)=0, then x=0 or π but x=0 is not in the given domain

cos(x)=1/2, then x= π/3 or 5π/3

Thus x could be π/3, π or 5π/3

Answer 2

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