Home
Class 12
MATHS
f(x)=1+[cosx]x,"in "0ltxle(pi)/(2)...

`f(x)=1+[cosx]x,"in "0ltxle(pi)/(2)`

A

has a minimum value 0

B

has a maximum value 2

C

is continuos in `[0,(pi)/(2)]`

D

is not differentiable at `x=(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C: D
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|28 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 1|1 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 4|15 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexltpi):} such that f is periodic with period pi . Then which of the following is not true?

Let f(x)={:{(x^(2)+4x",",-3lexle0),(-sinx",",0ltxle(pi)/(2)),(-cosx-1",",(pi)/(2)ltxlepi):} then

If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):} , where [.] and {.} denotes greatest integer and fractional part of x, then a. f'(1^(-)) = 2 b. f'(1^(+)) = 2 c. f'(1^(-)) = -2 d. f'(1^(+)) = 0

If f(x)=(2cosx-sin2x)/((pi-2x)^(2)) , g(x)=(e^(-cosx)-1)/(8x-4pi) h(x)=f(x) for x lt pi/2 h(x) = g(x) for x gt pi/2 then which of the following holds?

Find the intervals in which the function 'f' given by: f(x) = sin x-cosx , 0 le x le 2pi is strictly increasing or decreasing.

Find the intervals in which the function f given by f(x) = sinx + cosx, 0lexle2pi is increasing

If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le 0):} ,( x-1, 0 lt x le 1),("in"x, x gt1):}

Determine the value of constant A so that the function f(x)={((1-cosx)/(x^(2))" , "xne0),(A" , "x=0):} is continuous at x=0