Home
Class 12
MATHS
Let f:[a-> b] be a function such that fo...

Let `f:[a-> b]` 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`

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

f has a local maximum at x = a and local minimum at x = b. Then -

If a function f(x) has f^(prime)(a)=0 and f^(primeprime)(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.

If f(x)=e^(px+q) ,then shoq that f(a).f(b).f(c)=f(a+b+c).e^(2q)

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

If f(x)=e^(px+q) , then show that f(a).f(b).f(c)=f(a+b+c).e^(2q)

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal. (a) f^(prime)(c) (b) 1/(f^(prime)(c)) (c) f(c) (d) none of these

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

If f(x)=e^(px+q) [p and q are constants], show that, f(a).f(b).f(c)=f(a+b+c).e^(2q)

Let f:(-oo,oo) -> [0,oo) be a continuous function such that f(x+y)=f(x)+f(y)+f(x)f(y),AAx in Rdot Also f'(0)=1. Then [f(2)] equal ([dot] represents the greatest integer function ) a. 5 b. 6 c. 7 d. 8

Let f(x) be a polynomial function of second degree. If f (1) =f(-1) and a,b,c are in A.P. then f (a) , f'(b) , f'(c ) are in-

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Find the derivative of the function given by f(x)=(4sinx-2x-xcosx)/(2+...

    Text Solution

    |

  2. The coordinates of the point(s) on the graph of the function f(x)=(x^3...

    Text Solution

    |

  3. Let f:[a-> b] be a function such that for c in (a , b),f^(prime)(c)=f^...

    Text Solution

    |

  4. Which of the following pair(s) of curves is/are orthogonal?

    Text Solution

    |

  5. If (2, 3, 5) is one end of a diameter of the sphere x^2+""y^2+""z^2...

    Text Solution

    |

  6. Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the poi...

    Text Solution

    |

  7. Prove that the following functions are strictly increasing: f(x)=log(1...

    Text Solution

    |

  8. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

    Text Solution

    |

  9. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

    Text Solution

    |

  10. If there is an error of k % in measuring the edge of a cube, then the...

    Text Solution

    |

  11. Prove that the function f(x)=(log)e(x^2+1)-e^(-x)+1 is strictly increa...

    Text Solution

    |

  12. The rate of change of the volume of a sphere w.r.t. its surface area, ...

    Text Solution

    |

  13. Prove that the function are increasing for the given intervals: f(x)=s...

    Text Solution

    |

  14. A man is moving away from a tower 41.6 m high at the rate of 2 m/sec. ...

    Text Solution

    |

  15. Prove that the function are increasing for the given intervals: f(x)=s...

    Text Solution

    |

  16. A man 2m tall, walks at the rate of 1 2/3m//s e c towards a street lig...

    Text Solution

    |

  17. Find the least value of k for which the function x^2+k x+1 is an inc...

    Text Solution

    |

  18. At the point P(a , a^n) on the graph of y=x^n ,(n in N), in the first...

    Text Solution

    |

  19. If f:[0,oo]toR is the function defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(...

    Text Solution

    |

  20. Find the coordinates of a point the parabola y^(2)=8x whose distance f...

    Text Solution

    |