Home
Class 12
MATHS
If f(x)=x^3+a x^2+b x+c has a maximum at...

If `f(x)=x^3+a x^2+b x+c` has a maximum at `x=-1` and minimum at `x=3` . Determine `a ,\ b` and `c` .

Text Solution

Verified by Experts

Given function: f(x) = x3 + ax2 + b x + c
Differentiating with respect to x
`f ‘(x) = 3x^2 + 2ax + b`
It is given that f (x) is maximum at x = -1
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA|Exercise Solved Examples And Exercises|52 Videos

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA|Exercise Solved Examples And Exercises|113 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^(3)+ax^(2)+bx+c is minimum at x=3 and maximum at x=-1, then

If f(x)=x^(3)+ax^(2)+bx+c is minimum at x=3 and maximum at x=-1, then-

Let f(x)=x^(3)+3x^(2)-9x+2. Then,f(x) has a maximum at x=1 (b) a minimum at x=1( c) neither a maximum nor a minimum at x=-3(d) none of these

Which one of the following statements is correct in respect of the function f(x)=x^(3)sin x?(a) It has local maximum at x=0. (b) It has local minimum at x=0. (c) It has neither maximum nor minimum at x=0.( d) It has maximum value 1.

The function f(x)=2x^(3)-3(a+b)x^(2)+6abx has a local maximum at x=a , if

if f(x)=(x^(3))/(3)-x^(2)+(1)/(5) find maximum and minimum value of f(x)

Let f(x) be a polynomial of degree 3 such that f(-2)=5, f(2)=-3, f'(x) has a critical point at x = -2 and f''(x) has a critical point at x = 2. Then f(x) has a local maxima at x = a and local minimum at x = b. Then find b-a.

Let f and g be two differentiable functions defined from R->R^+. If f(x) has a local maximum at x = c and g(x) has a local minimum at x = c, then h(x) = f(x)/g(x) (A) has a local maximum at x = c (B) has a local minimum at x = c (C) is monotonic at x = c 1.a g(x) (D) has a point of inflection at x = c

Let f(x)=x^(3)+ax^(2)+bx+c , where a, b, c are real numbers. If f(x) has a local minimum at x = 1 and a local maximum at x=-1/3 and f(2)=0 , then int_(-1)^(1) f(x) dx equals-

RD SHARMA-MAXIMA AND MINIMA-Solved Examples And Exercises
  1. Find the maximum and minimum values of the function f(x)=4/(x+2)+x ...

    Text Solution

    |

  2. Find the maximum and minimum values of the function f(x)=tanx-2x .

    Text Solution

    |

  3. If f(x)=x^3+a x^2+b x+c has a maximum at x=-1 and minimum at x=3 . Det...

    Text Solution

    |

  4. Prove that f(x)=sinx+sqrt(3)cosx has maximum value at x=pi/6 .

    Text Solution

    |

  5. Find the maximum and minimum values of f(x)=2x^3-24 x+107 in the in...

    Text Solution

    |

  6. Find the maximum and minimum values of f(x)=x+sin2x .

    Text Solution

    |

  7. Find the maximum and minimum values of f(x)=sinx+1/2cos2x in [0,\ p...

    Text Solution

    |

  8. Find the maximum and minimum values of f(x)=x^(50)-x^(20) in the in...

    Text Solution

    |

  9. Find the maximum and minimum values of f(x)=x+sin2x in the interval...

    Text Solution

    |

  10. Find the difference between the greatest and least values of the fun...

    Text Solution

    |

  11. Show that f(x)=sinx(1+cosx) is maximum at x=pi/3 in the interval [0,\ ...

    Text Solution

    |

  12. Find the absolute maximum value and the absolute minimum value of f(...

    Text Solution

    |

  13. Find the absolute maximum value and the absolute minimum value of f...

    Text Solution

    |

  14. Find both the maximum and the minimum value of 3x^4-8x^3+ 12 x^2-48 x+...

    Text Solution

    |

  15. Find the absolute maximum and absolute minimum values of f(x)=4x-(x...

    Text Solution

    |

  16. Find the absolute maximum and absolute minimum values of f(x)=(x-1)...

    Text Solution

    |

  17. Find the absolute maximum and absolute minimum values of f(x)=3x^4-...

    Text Solution

    |

  18. Find the absolute maximum and the absolute minimum values of the follo...

    Text Solution

    |

  19. Find the maximum value of 2x^3-24 x+107 in the interval [1,\ 3] . F...

    Text Solution

    |

  20. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |