`{:(f(x) = cos x and H_(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)/(2) = (pi)/(2)-x,(pi)/(2) lt x le pi),(f(x) = cos x and H_(2) (x) = max {f(t), o le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x","(pi)/(2) lt x le pi),(g(x) = sin x and H_(3)(x) = min{g(t),0 le t le x},),(0 le x le (pi)/(2)=(pi)/(2) - x, (pi)/(2) le x le pi),(g(x) = sin x and H_(4)(x) = max{g(t),0 le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x, (pi)/(2) lt x le pi):}`
Which of the following is true for `H_(3) (x)`?

Options

A. H(x) is continuous and derivable in [0, 3]
B. H(x) is continuous but not derivable at `x = (pi)/(2)`
C. H(x) is neither continuous nor derivable at `x = (pi)/(2)`
D. maximum value of H(x) in [0, 3] is 1

Answer

A, D