Home
Class 12
MATHS
If a function f(x) has f^(prime)(a)=0a n...

If a function `f(x)` has `f^(prime)(a)=0a n df^(a)=0,` then (a) `x=a` is a maximum for `f(x)` (b)`x=a` is a minimum for `f(x)` (c)can not conclude anything about its maxima and minima (d)`f(x)` is necessarily a constant function.

A

x=a is a maximum for f(x)

B

x=a is a minimum for(x)

C

it is difficult to say (a) and (b)

D

f(x) is necessarily a constant function

Text Solution

Verified by Experts

The correct Answer is:
3

consider function `x^(3)-x^(4),x^(4)`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|48 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Numerical Value Type|24 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.7|5 Videos
  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos
  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a ,f(x) has a (a) minimum value (b) maximum value (c)not an extreme point (d) extreme point

Lert f:[a , b]vec be a function such that for c in (a , b),f^(prime)(c)=f^(ii) (c)=f^(iii) (c)=f^(iv) (c)=f^v(c)=0. Then f (a)has a local extermum at x=cdot f (b)has neither local maximum nor minimum at x=c f (c)is necessarily a constant function (d)it is difficult to say whether a)or(b)dot

A function f such that f'(a)=f''(a)=….=f^(2n)(a)=0 , and f has a local maximum value b at x=a ,if f (x) is

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)

Let f(x) be a cubic function such that f'(1)=f''(2)=0 . If x=1 is a point of local maxima of f(x), then the local minimum value of f(x) occurs at

A polynomial function f(x) is such that f'(4)= f''(4)=0 and f(x) has minimum value 10 at x=4 .Then

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; and 6x+5x^2,x >0 Then at x=0,f(x) (a) has a local maximum (b) has a local minimum (c) is discontinuous (d) none of these

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

    Text Solution

    |

  2. If f(x)=alog|x|+b x^2+x has extreme values at x=-1 a n d a t x=2, then...

    Text Solution

    |

  3. If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then (a) x=a is a...

    Text Solution

    |

  4. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  5. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Let f(x)={(|x|,for 0<|x|lt=2), (1,"for"x=0):} Then at x=0, f(x) has ...

    Text Solution

    |

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

    Text Solution

    |

  10. If f(x)={(sin(x^(2)-3x),xle0 6x+5x^(2),xgt0 then at x=0, f(x) is?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. The function f(x)=(ln(pi+x))/(ln(e+x)) is

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let the function f(x) be defined as follows:f(x)= x^3 +x^2 −10x,−1≤x<...

    Text Solution

    |