Home
Class 12
MATHS
The functions defined by f(x)="max" {x^(...

The functions defined by `f(x)="max" {x^(2),(x-1)^(2),2x(1-x)}, 0lexle1`

A

is differentiable for all x

B

is differentiable for all x except at one point

C

is differentiable for all x except at two points

D

is not differentiable at more than two points

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 2 (Level-I) Objective Problems | JEE Main|15 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 2 (Level-II) Multiple Correct | JEE Advanced|8 Videos

  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|15 Videos

  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

  • DIFFERENTIAL EQUATION

    MOTION|Exercise Exercise 4|29 Videos

Similar Questions

Explore conceptually related problems

Find the equivalent definition of f(x)=max{x^(2),(1-x)^(2),2x(1-x)} where 0<=x<=1

A function f defined by f(x)=In(sqrt(x^(2)+1-x)) is

The function f:R rarr R defined as f(x)=(x^(2)-x+1)/(x^(2)+x+1) is

Consider the function f(x)=max. [(x^(2) , (1-x)^(2) , 2x(1-x))] , x in [0,1] The interval in which f(x) is increasing, is

Consider the function f(x)=max x^(2), [((1-x)^(2),2x(1-x))],x in [0,1] The interval in which f(x) is decreasing is

The minimum value of the function defined by f(x)=max(x,x+1,2-x) is

The function f defined by f(x)=(4sinx-2x-xcosx)/(2+cosx),0lexle2pi is :

Discuss the applicability of Rolle's theorem on the function given by f(x) = {{:(x^(2)+1,if0lexle1),(3-x,if1lexle2):}

Let the function f(x) be defined as follows: f(x)={x^(3)+x^(2)-10x,-1lexle0 cosx,0lexlepi//2 1+sin x, pi//2 lexlepi

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

MOTION-DIFFERENTIABILITY-Exercise - 1 Objective Problems | JEE Main
  1. if f(x) = x( sqrtx + sqrt(x+1)), then

    Text Solution

    |

  2. Let f (x)= [{:((x(3e^(1//x)+4))/(2 -e^(1//x)),,,( x ne 0)),(0 ,,, x=0)...

    Text Solution

    |

  3. If f(x)=x/(sqrt(x+1)-sqrtx) be a real valued function, then

    Text Solution

    |

  4. If f(x)=[tan^(2)x] then (where [ast] denotes the greatest integer func...

    Text Solution

    |

  5. Let f(x) be defined in [-2,2] by f(x) = { max(sqrt4-x^2),sqrt(1+x^2)),...

    Text Solution

    |

  6. The function f(x)=sin^(-1)(cosx) is

    Text Solution

    |

  7. Let f(x)=(abs(x))/(sinx) for xne0 "and" f(0)=1 "then",

    Text Solution

    |

  8. If f(x) = [x^2] + sqrt({x}^2, where [] and {.} denote the greatest int...

    Text Solution

    |

  9. If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 the...

    Text Solution

    |

  10. If f(x) is differentiable everywhere, then which one of the following ...

    Text Solution

    |

  11. Let f(x+y)=f(x)*f(y)AAx , y in R,suppose that f(3)=3 and f^(prime)(0...

    Text Solution

    |

  12. LEt F: R->R is a differntiable function f(x+2y) =f(x) + f(2y) +4xy for...

    Text Solution

    |

  13. Suppose that f is a differentiable function with the property that f(x...

    Text Solution

    |

  14. "Let" f(x+y)=f(x)f(y) "for all x,y, where" f(0)ne0. If f'(0)=2, then f...

    Text Solution

    |

  15. The functions defined by f(x)="max" {x^(2),(x-1)^(2),2x(1-x)}, 0lexle1

    Text Solution

    |

  16. If f is an even function such that (lim)(hvec0)(f(h)-f(0))/h has some ...

    Text Solution

    |

  17. Let f: R to R be a function defined byf(x)="min" {x+1,|x|+1}. Then, wh...

    Text Solution

    |