Home
Class 12
MATHS
L e tf(x)={|x|,for0<|x|lt=2 1,forx=0 Th...

`L e tf(x)={|x|,for0<|x|lt=2 1,forx=0` Then at `x=0,f` has a local maximum (b) no local maximum a local minimum (d) no extremum

A

a local maximum

B

no local maximum

C

a local minimum

D

no extremum

Text Solution

Verified by Experts

The correct Answer is:
1


From the graph `f(0^(+))ltf(0^(+))and f(0^(-))lt0` Thus x=0 is the point of maxima
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|40 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.7|5 Videos
  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos
  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2 If f(x) has a local maxima at x=3/2 , then greatest value of |4a| is _________

L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

L e tf(x)={x^2+3x ,-1lt=x<0-sinx ,0lt=x

L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive constant. Find the interval in which f^(prime)(x) is increasing.

L e tf(x)={x^3+x^2+3x+sinx|(3+s in1/x ,),x!=0. 0x=0 then the number of point where f(x) attains its minimum value is_____

Suppose that f is an even, periodic function with period 2,a n dt h a tf(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is(where [.] represents the greatest integer function) ______

Suppose that f is an even, periodic function with period 2,a n dt h a tf(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is(where [.] represents the greatest integer function) ______

L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2 Then at x=1/2, which of the following is/are not true? (a) f has a local maxima (b) f has a local minima (c) f has an inflection point. (d) f has a removable discontinuity.

L e tf(x)=x^3=(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) os____

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  1. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=pa n dx=q ...

    Text Solution

    |

  2. Let P(x)=a0+a1x^2+a2x^4++an x^(2n) be a polynomial in a real variable ...

    Text Solution

    |

  3. L e tf(x)={|x|,for0<|x|lt=2 1,forx=0 Then at x=0,f has a local maximu...

    Text Solution

    |

  4. If f(x)=x^3+b x^2+c x+d and 0 le b^2 le c , then a)f(x) is a strictly ...

    Text Solution

    |

  5. If f(x)={(sin(x^(2)-3x),xle0 .^x+5x^(2),xgt0

    Text Solution

    |

  6. The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...

    Text Solution

    |

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

    Text Solution

    |

  8. The true set of real values of x for which the function f(x)=xlnx-x+1 ...

    Text Solution

    |

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

    Text Solution

    |

  10. The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decrea...

    Text Solution

    |

  11. If the function f(x)=2x^3-9a x^2+12 x^2x+1,w h e r ea >0, attains its ...

    Text Solution

    |

  12. Let f(x)={x+2,-1lelt0 1,x=0 (x)/(2),0ltxle1

    Text Solution

    |

  13. If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    Text Solution

    |

  14. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |

  15. Let the function f(x) be defined as follows: f(x)={x^(3)+x^(2)-10x,-...

    Text Solution

    |

  16. Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x...

    Text Solution

    |

  17. F(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)

    Text Solution

    |

  18. Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 le...

    Text Solution

    |

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

    Text Solution

    |

  20. The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

    Text Solution

    |