Home
Class 12
MATHS
Q. Let f (x)=sin^3x+ lambdasin^2x where...

Q. Let `f (x)=sin^3x+ lambdasin^2x` where `(pi)/2 ltxlt (pi)/2.` The interval in which `lambda`should lie in order that f (x) has exactly one minimum and exactly one maximum is

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

Q.Let f(x)=sin^(3)x+lambda sin^(2)x where (pi)/(2)

Let f(x)=sin^(3)x+lambda sin^(2)x where -pi//2ltxltpi//2. Find the intervals in which lambda should lie in order that f(x) has exactly one minimum.

Let f(x)=sin^(3)x+lambda sin^(2)x,-(pi)/(2)

Let f(x)=2sin^(3)x+lamdasin^(2)x,-(pi)/2ltxlt(pi)/2 . If f(x) has exactly one minimum and one maximum, then lamda cannot be equal to

Let f (x) = x^(2) , x in [-1 , 2) Then show that f(x) has exactly one point of local minima but global maximum is not defined.

If f(x)=x ln x-2, then show that f(x)=0 has exactly one root in the interval (1,e).

Show that f(x)=sin x(1+cos x) is maximum at x=(pi)/(3) in the interval [0,pi] .

Show that f(x)=sin x(1+cos x) is maximum at x=(pi)/(3) in the interval [0,pi]

The set of all real value of lambda for which the functio f(x) = (1-cos^(2)x) . (lambda + sinx) , xe(-(pi)/(2) , (pi)/(2)) has exactly one maxina and exactly one minima is

A DAS GUPTA-Maxima and Minima-EXERCISE
  1. Q. Let f (x)=sin^3x+ lambdasin^2x where (pi)/2 ltxlt (pi)/2. The inte...

    Text Solution

    |

  2. Find the maxima and minimum value of the function y = 40/(3x^(4)+ 8x^(...

    Text Solution

    |

  3. f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))

    Text Solution

    |

  4. Show that f(x) = sqrt(e^(x^(2))-1) has its extremum at x = 0. Also me...

    Text Solution

    |

  5. Using examples, prove that the conditiondy/dx = 0 is neither a necessa...

    Text Solution

    |

  6. Let f(x) = x ^3 - 12x. Prove that the equation x^3 - 12x - k = 0 has a...

    Text Solution

    |

  7. If y=a log x +bx^(2)+x has its exteme values at x=-1 and x=2, then fin...

    Text Solution

    |

  8. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,-1), find the value ...

    Text Solution

    |

  9. Find the shortest distance of the point (0, c) from the parabola y=x^...

    Text Solution

    |

  10. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

    Text Solution

    |

  11. Given an interior point A on the axis of the parabola y ^2 = 2px, (p >...

    Text Solution

    |

  12. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

    Text Solution

    |

  13. The parametric equations of the curve are x=2t(t^2+3)-3t^2, y=2t(t^2+3...

    Text Solution

    |

  14. A function is defined parametrically as follows :x=t^5-5t^3-20 t+7y=4t...

    Text Solution

    |

  15. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

    Text Solution

    |

  16. A 12-cm-long wire is bent to form a triangle with one of the angles as...

    Text Solution

    |

  17. The largest area of a rectangle which has one side on the x-axis and t...

    Text Solution

    |

  18. Three sides of a trapezium are each equal to k cm. Find the greatest p...

    Text Solution

    |

  19. A statue 4 meters high sits on a column 5.6 meters high . How far f...

    Text Solution

    |

  20. A wire of length l is cut into two parts. One part is bent into a circ...

    Text Solution

    |

  21. A point P is given on the circumference of a circle of radius rdot Cho...

    Text Solution

    |