Question

Which of the following is true about the graph of f on the interval [0,pi]? f(x)=x+sin(2x)-2

a) f(x) is increasing on the interval ((1/3)pi, (2/3)pi)
b) f(x) is concave up on the interval (0, (2/3)pi)
c) f(x) is decreasing on the interval (0,pi)
d)f(x) has a local max at the point ((1/3)pi , (1/3)pi+(1/2)sqrt(3)-2)
e)f(x) has a point of inflection at (0,-2)

Answer 1

I know the derivative is f'(x)= 1+2cos(2x) and the second derivative is f''(x)=-4sin(2x)

Answer 2

Also I know to find the critical numbers I must set the first derivative equal to zero or find where it s undefined so

\[1+2\cos(2x)=0\]
\[2\cos(2x)=-1\]
\[\cos(2x)=\frac{ -1 }{ 2 }\]

But I dont know how to find the critical numbers from here