Home
Class 12
MATHS
Which of the following function has poin...

Which of the following function has point of extremum at `x=0?`
(a) `f(x)=e^(-|x|)`
(b) `f(x)="sin"|x|`
(c) `f(x)={x^2+4x+3,x<0; -x , xgeq0`
(d) `f(x)={|x|,x<0; {x},0lt=x<1` (where `{x}` represents fractional part function).

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 following function/functions has/have point of inflection? f(x)=x^(6/7) (b) f(x)=x^6 f(x)=cosx+2x (d) f(x)=x|x|

Which of the following functions is the inverse of itself? (a) f(x)=(1-x)/(1+x) (b) f(x)=5^(logx) (c) f(x)=2(x(x-1)) (d) None of these

if f(x)=e^(x)+4x then f'(x)=

Which of the following function is non-differentiable in domain? f(x)=(x-2)/(x^2+3) (b) f(x)=log|x| f(x)=x^3logx (d) f(x)=(x-3)^(3/5)

The function f(x)=sinxcos^(2)x has extremum at -

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

For which of the following functions f(0) exists such that f(x) is continuous at x=0 f(x)=1/((log)_e|x|) b. f(x)=(cos((sin|x|)/x)) c. f(x)=x sin(pi/x) d. f(x)=1/(1+2^(cot x))

Which of the following function is (are) even, odd, or neither? (a). f(x)=x^2sinx (b). f(x)=log((1-x)/(1+x)) (c). f(x)=log(x+sqrt(1+x^2)) (d). f(x)=(e^x+e^(-x))/2

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

Let A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature of each of the following functions. (i) f(x) = |x| " (ii) " f(x)=x|x| (iii) f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The function f(x)=x^2+lambda/x has a (a)minimum at x=2iflambda=16 ...

    Text Solution

    |

  2. Which of the following is true about point of extremum x=a of function...

    Text Solution

    |

  3. Which of the following function has point of extremum at x=0? (a) f(...

    Text Solution

    |

  4. Which of the following hold(s) good for the function f(x)=2x-3x^(2/3) ...

    Text Solution

    |

  5. For the function f(x)=(e^x)/(1+e^x), which of the following hold good...

    Text Solution

    |

  6. The global maximum value of f(x)=(log)(10)(4x^3-12 x^2+11 x-3),x in [2...

    Text Solution

    |

  7. If a^(2)x^(4)+b^(2)y^(4)=c^(6)(a,b,x,y,cgt0) then the maximum value of...

    Text Solution

    |

  8. The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e...

    Text Solution

    |

  9. The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 ...

    Text Solution

    |

  10. Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of...

    Text Solution

    |

  11. The maximum slope of the curve y=-x^3+3x^2+9x-27 is (a) 0 (b) 12 (c)...

    Text Solution

    |

  12. The maximum value of f(x)=x/(1+4x+x^2) is -1/4 (b) -1/3 (c) 1/6 (d)...

    Text Solution

    |

  13. Let f(x)={(x+2,-1lexle0),(1,x=0),(x/2,0ltxle1):} Then on [-1,1] this f...

    Text Solution

    |

  14. The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the ...

    Text Solution

    |

  15. The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c...

    Text Solution

    |

  16. The function f(x)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5 d...

    Text Solution

    |

  17. Let f:IRrarrIR be defined as f(x)=|x|+|x^2-1|.The total number of poin...

    Text Solution

    |

  18. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  19. Find the current through an ideal p- n junction diode asshown is figur...

    Text Solution

    |

  20. Given that E and F are events such that P (E) = 0.6, P (F) = 0.3 and P...

    Text Solution

    |