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 `x=a` is a maximum for `f(x)` `x=a` is a minimum for `f(x)` it is difficult to say `(a)a n d(b)` `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|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

If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(a)>0, then at x=a ,f(x) is minimum (b) maximum 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^"(c)=f^"'(c)=f^(i v)(c)=f^v(c)=0. Then f (a)has a local extermum at x=c dot (b) f has neither local maximum nor minimum at x=c (c) f is necessarily a constant function (d)it is difficult to say whether (a)or(b)dot

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

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

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

Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. Then f is

A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x+1)),AAx > -1. If f(0)=5, then f(x) is

If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n f(x) is an odd function f(x) has range R f(x) has at least one real root f(x) is a monotonic function.

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  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 its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

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

    Text Solution

    |

  4. The function f(x) = sin ^(4)x+ cos ^(4)x increases, if

    Text Solution

    |

  5. The function f(x) = sin ^(4)x+ cos ^(4)x increases, if

    Text Solution

    |

  6. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=pa n dx=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. L e tf(x)={|x|,for0<|x|lt=2 1,forx=0 Then at x=0,f has a local maximu...

    Text Solution

    |

  9. 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

    |

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

    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 increasing in (0,oo) decrea...

    Text Solution

    |

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

    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,-...

    Text Solution

    |