Home
Class 12
MATHS
Let f(x) be a function such that f'(a) n...

Let f(x) be a function such that `f'(a) ne 0` . Then , at x=a, f(x)

A

f(x) cannot have maximum at ` x = a`

B

f(x) cannot be minimum at `x = a`

C

f(x) must have neither a maximum nor a minimum at `x = a`.

D

none of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Maxima and Minima

    A DAS GUPTA|Exercise EXERCISE|59 Videos
  • Main Tests

    A DAS GUPTA|Exercise Exercise|8 Videos
  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f(x) be a continuous function such that f(0)=1 and f(x)=f((x)/(7))=(x)/(7)AA x in R then f(42) is

[" Let "f(x)" be a function such that "],[f''(x)=f(x)" and "f'(0)=f(0)=0" .The "],[" value of "(f(x))/(4-f(x))dx" is equal to "]

Let f(x) be a function such that f'((1)/(x))+x^(3)f'(x)=0. What is int_(-1)^(1)f(x)dx

Let f be a function such that f(x)>0 Assume that f has derivatives of all orders and that In f(x)=f(x)int_(0)^(x)f(t)dt find f^(2)(0)

Let f(x) be a function such that,f(0)=f'(0)=0,f''(x)=sec^(4)x+4 then the function is

Let f be a real function such that f(x-y), f(x)f(y) and f(x+y) are in A.P. for all x,y, inR. If f(0)ne0, then

Let /be a function such that 3f(x) + 22f(1/x) = 7x, AA x ne 0 , then for each x ne 0 , f(x) is equal to

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

A DAS GUPTA-Maxima and Minima-EXERCISE
  1. What is the area of the largest triangle that can be inscribed in a se...

    Text Solution

    |

  2. x and y be two variables such that xgt0 and xy=1. Then the minimum val...

    Text Solution

    |

  3. The value of a so that the sum of the squares of the roots of the equa...

    Text Solution

    |

  4. Twenty metres of wire is available for fencing off a flower-bed in ...

    Text Solution

    |

  5. The total cost of making n pocket radios per day is Rs{(n^2)/4 +35n + ...

    Text Solution

    |

  6. A telephone company in a town has 500 subscribers on its list and c...

    Text Solution

    |

  7. If P(x) = a 0 + a 1 x ^(2) + a 2 x^(4) + … + a n x ^(2n) is a polyn...

    Text Solution

    |

  8. Find the minimum length of radius vector of the curve (a^2)/(x^2)+(b^...

    Text Solution

    |

  9. A right cylindrical vessel of a given capacity is formed using least p...

    Text Solution

    |

  10. Let f(x) =(x-1)^p.(x-2)^q where p > 1, q > 1. Each critical point of f...

    Text Solution

    |

  11. The point (0, 3) is closest to the curve x^2 = 2y at

    Text Solution

    |

  12. For the function f(x)=xe^x, the point

    Text Solution

    |

  13. Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

    Text Solution

    |

  14. N Characters of information are held on magnetic tape, in batches of x...

    Text Solution

    |

  15. The function f(x) = x^2+a/xcannot have a maximum at x = -3 for any rea...

    Text Solution

    |

  16. Find the maximum slope of the curve y=-x^3+3x^2+2x-27 .

    Text Solution

    |

  17. Two points A(1, 4) & B(3, 0) are given on the ellipse 2x^(2) + y^(2) =...

    Text Solution

    |

  18. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

  19. P is a variable point on the curve y= f(x) and A is a fixed point in...

    Text Solution

    |

  20. The fuel charges for running a train are proportional to the square of...

    Text Solution

    |