Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 15

Given the function h(x)=sin^2(x)+cos(x) in the interval 0We have to find the critical numbers of the function.
First take the derivative of the function and equate it to zero.
We get,
h'(x)=2sin(x)cos(x)-sin(x)=0
sin(x)(2cos(x)-1)=0
sin(x)=0 or 2cos(x)-1=0
sin(x)=0 implies x= npi
i.e we get x= pi in the interval 0Now,
2cos(x)-1=0 implies cos(x)=1/2
So x= pi/3 and 5pi/3 (in the interval 0Hence the critical points are x=pi/3, pi and (5pi)/3

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