Home
Class 12
MATHS
Let f(x)=sin^3x+lambdasin^2x ,pi/2<x<pi/...

Let `f(x)`=`sin^3x+lambdasin^2x` ,`pi/2`<`x`<`pi/2dot` Find the intervals in which `lambda` should lie in order that `f(x)` has exactly one minimum and exactly one maximum.

A

`(-3//2,3//2)`

B

`(-2//3 ,2//3)`

C

`R`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-2 Part II|21 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-2 Part III|19 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise Part II -1F|4 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

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

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)=-sin^3x+3sin^2x+5 on [0,pi/2] . Find the local maximum and local minimum of f(x)dot

Let f(x)={(1-sin^3x)/(3cos^2x) if x pi/2 find a and b. .

Separate the intervals of monotonocity of the function: f(x)=-sin^3x+3sin^2x+5,x in [-pi/2,pi/2]dot

Let f(x)=sinx+2cos^2x , x in [pi/6,(2pi)/3] , then maximum value of f(x) is

Let f(x) = sin^(3)x - 3 sinx + 6, AA x in (0, pi) .The number of local maximum/maxima of the function f(x) is

Let f(x)=|x|+|sin x|, x in (-pi//2,pi//2). Then, f is

The period of the function f(x)=c^((sin^2x) +sin^2 (x+pi/3)+cosxcos(x+pi/3)) is (where c is constant)

Statement 1: Let f(x)=sin(cos x) \ i n \ [0,pi/2] . Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Exersise-2 Part I
  1. "Let "f(x) ={ underset( x^(2) +8 " "." "x ge0)(-x^(2)" "." "x lt0)...

    Text Solution

    |

  2. Minimum distance between the curves f(x)=e^x and g(x)=ln x is

    Text Solution

    |

  3. The point(s) on the parabola y^2 = 4x which are closest to the circlex...

    Text Solution

    |

  4. Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R , where ...

    Text Solution

    |

  5. If f:[1,10]->[1,10] is a non-decreasing function and g:[1,10]->[1,10] ...

    Text Solution

    |

  6. If f(x)=|ax-b|+c|x| is stricly increasing at atleast one point of non ...

    Text Solution

    |

  7. If g(x) is a curve which is obtained by the reflection of f(x) = (e^x...

    Text Solution

    |

  8. The set of values of p for which the points of extremum of the functio...

    Text Solution

    |

  9. The values of parameter a for which the point of minimum of the functi...

    Text Solution

    |

  10. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

    Text Solution

    |

  11. Let f(x)=sin^3x+lambdasin^2x ,pi/2<x<pi/2dot Find the intervals in whi...

    Text Solution

    |

  12. "Let "f(x) ={underset(-2x + log(2) (b^(2)-2), x gt1)(x^(3) -x^(2) +10 ...

    Text Solution

    |

  13. Four points A, B, C, D lie in that order on the parabola y = ax^2 +bx+...

    Text Solution

    |

  14. In a regular triangular prism the distance from the centre of one ...

    Text Solution

    |

  15. The maximum area of the rectangle whose sides pass through the vertice...

    Text Solution

    |

  16. Statement 1: ABC is given triangle having respective sides a,b,c. D,E,...

    Text Solution

    |

  17. if f(x)=(x -4) (x-5) (x-6) (x-7) then, (A) f'(x) =0 has four roots (...

    Text Solution

    |

  18. Show that the square roots of two successive natural numbers greater ...

    Text Solution

    |

  19. If Rolle's theorems applicable to the function f(x)=ln x/x, (x> 0) ove...

    Text Solution

    |

  20. if f(x) be a twice differentiable function such that f(x) =x^(2) " fo...

    Text Solution

    |