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The function f(x) = 1 + x (sin x) [cos x...

The function `f(x) = 1 + x (sin x) [cos x], 0 lt x le (pi)/(2)` (where [.] is G.I.F.)

A

is continuous on `(0, (pi)/(2))`

B

is strictly increasing in `(0, (pi)/(2))`

C

is strictly decreasing in `(0, (pi)/(2))`

D

has global maximum value 2

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The function f(x) =(sin x) +[cos x], 0 lt x le pi//2

    A
    is continuous on `(0, pi//2)`
    B
    is strictly decreasing in `(0, pi//2)`
    C
    is stricitly increasing in `(0, pi//2)`
    D
    has global maximum value 2

  • f(x) = 1 + 2 sin x + 3 cos^2 x, ( 0 le x lt (2pi)/3) is

    A
    Min. at `x = 90^@`
    B
    Max. at `x = sin^(-1) 1/sqrt3`
    C
    Min. at `x = 30^@`
    D
    Max. at `x = sin^(-1) (1/3)`

  • The function f(x)=cos x, 0 le x le pi is

    A
    decreasing
    B
    increasing
    C
    neither increasing nor decreasing
    D
    increasing for `0 le x le pi`

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