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Q. Let f(x)=cos x $ H(x)=[min [f(t) 0&l...

Q. Let `f(x)=cos x` $ `H(x)=[min [f(t) 0<=t<=x` for `0<=x<=pi/2` , `pi/2-x` for `pi/2 ltx <="3`

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

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The correct Answer is:
A, D
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Q.Let f(x)=cos x$H(x)=[min[f(t)0<=t<=x for 0<=x<=(pi)/(2),(pi)/(2)-x for (pi)/(2)

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{:(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_(4)(x) ?

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