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see graph of sin function
or we can use dufferentiation method
derivative of sinx = cosx
put cosx = 0
x= (2n+1) π/2
where n € I set of integers
in range 0 to 4π
x = π/2, 3π/2 for n=0, 1
5π/2 greater then 4π
double derivative of sinx = - sinx
now π/2 lies in first quadrant and 3π/2 lies in third quadrant and sin function positive in 2nd quadrant and negative in third quadrant
we have double derivative = - sinx
so d2x/dx2 > 0 for x = 3π/2 minima
and
d2x/dx2 < 0 for x= π/2 maxima
hope it helps
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