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{:(f(x) = cos x and H(1)(x) = min{f(t), ...

`{:(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_(1) (x)`?

A

Continuous and derivable in `[0, pi]`

B

Continuous but not derivable at `x = (pi)/(2)`

C

Neither continuous nor derivable at `x = (pi)/(2)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
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