Home
Class 12
MATHS
Statement 1: f(x)=|x-1|+|x-2|+|x-3| has ...

Statement 1: `f(x)=|x-1|+|x-2|+|x-3|` has point of minima at `x=3.` Statement 2: `f(x)` is non-differentiable at `x=3.`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Which of the function is non-differential at x=0? f(x)=|"x"^3|

Number of points at which f(x) = |x^2+x|+|x-1| is non-differentiable is

Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum nor minimum at x=2. Statement 2: If a function x=2 is a point of inflection, then it is not a point of extremum.

Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima for a<-2. Statement 2: x^2+a x+1=0 has both roots positive for a<-2.

Consider the function f(x)=|x-2|+|x-5|,x in RR . Statement-I : f'(4)=0 . Statement-II : f is continuous is [2, 5], differentiable in (2, 5) and f(2)=f(5) .

Consider the function f(x) = |x-2|+|x-5|, Statement 1: f'(4)=0 Statement 2: differentiable in (2,5) and f(2)=f(5)

show that the function f(x)=abs(x-2)+abs(x-3) is not differentiable at x=2 and x=3

The function f(x)=x^(1/3)(x-1) has two inflection points, has one point of extremum, is non-differentiable, has range [-3*2^(-8/3),oo)

Number of points where f(x)=| x sgn(1-x^2)| is non-differentiable is a. 0 b. 1 c. 2 d. 3

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Assertion Consider the following statements in S and R S: Both sinx a...

    Text Solution

    |

  2. Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Stat...

    Text Solution

    |

  3. Statement 1: f(x)=|x-1|+|x-2|+|x-3| has point of minima at x=3. State...

    Text Solution

    |

  4. Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...

    Text Solution

    |

  5. Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x...

    Text Solution

    |

  6. Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima...

    Text Solution

    |

  7. If a function f(x) has f^(prime)(a)=0 and f^(primeprime)(a)=0, then (...

    Text Solution

    |

  8. The minimum value of 2^((x^2-3)^3+27) is (a) 2^(27) (b) 2 (c) 1 (d...

    Text Solution

    |

  9. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q ...

    Text Solution

    |

  10. The maximum value of ((logx)/x)is

    Text Solution

    |

  11. The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N, has a local minimum...

    Text Solution

    |

  12. Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...

    Text Solution

    |

  13. The equation e^(x-1)+x-2=0 as

    Text Solution

    |

  14. The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the i...

    Text Solution

    |

  15. If [.] denotes the greatest integer function then lim(x→0)​[x^2/(tanx....

    Text Solution

    |

  16. If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...

    Text Solution

    |

  17. The real number x when added to its inverse given the minimum value of...

    Text Solution

    |

  18. Statement 1: Let f(x)=sin(cos x) \ i n \ [0,pi/2]. Then f(x) is decr...

    Text Solution

    |

  19. Let f(x)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has (a) a maximum at x=1...

    Text Solution

    |

  20. Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f...

    Text Solution

    |