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

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

Text Solution

Verified by Experts

We have
`f(x)=2(x-1)(x-2)3+3(-1)2(x-2)^(2)2`
`=(x-1)(x-2)^(2)(5x-7)`
Sign schem of f(x) is as shown in the following figure

Clearly f(x) has point of maxima at x=1 and point of minima t `x=7//5`
Also sign of derivative is not changing at x=2 so it is not a point of extrema.
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Illustration|2 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.1|10 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

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^(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+sin^(3)(x+(2 pi)/(3))+sin^(3)(x+(4 pi)/(3)) then the primitive of f(x)w.r.t.x is

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

Let f(x)=|x|+|sinx|, x in (-pi/ 2,3pi/2). Then , f is

Statement 1: Let f(x)=sin(cos x) in [0,(pi)/(2)]* Then f(x) is decreasing in [0,(pi)/(2)] Statement 2:cos x is a decreasing function AA x in[0,(pi)/(2)]

Let f(x)={(1-s in^3x)/(3cos^2x) , if x pi/2 . If f(x) is continuous at x=pi/2 , find a and b .

Let f(x) = 2sin^3x-3sin^2+12sinx+5, 0lexlepi/2 Then f(x)is

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

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

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-JEE Advanced Previous Year
  1. Let f(x)=sin^3x+lambdasin^2x ,-pi/2<x<pi/2dot Find the intervals in wh...

    Text Solution

    |

  2. The function f:[0,3]vec[1, 29], defined by f(x)=2x^3-15 x^2+36 x+1, is...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b)...

    Text Solution

    |

  4. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |

  5. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  6. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

    Text Solution

    |

  7. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

    Text Solution

    |

  8. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

    Text Solution

    |

  9. Let f:R rarr(0,oo) and g:R rarr R be twice differntiable function such...

    Text Solution

    |

  10. If f:RR-> RR is a differentiable function such that f(x) > 2f(x) f...

    Text Solution

    |

  11. If f(x) = |{:( cos (2x) ,, cos ( 2x ) ,, sin ( 2x) ), ( - cos x,, cosx...

    Text Solution

    |

  12. Let f:(0,pi)rarrR be a twice differentiable fucntion such that lim(tra...

    Text Solution

    |

  13. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

    Text Solution

    |

  14. If the function d^(-x) f(X) assumes its minimum in the interval [0,1] ...

    Text Solution

    |

  15. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  16. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  17. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  18. A cylindrica container is to be made from certain solid material with ...

    Text Solution

    |