Home
Class 11
MATHS
Separate the intervals of monotonicity o...

Separate the intervals of monotonicity of the following functions :
`f(x) = -sin^(3)x + 3 sin^(2)x + 5, x in [-pi//2, pi//2]`

Text Solution

Verified by Experts

The correct Answer is:
`(-pi//2, 0)`
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.1 (Long Answer Questions)|24 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.2 (Long Answer Questions)|36 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Examples|3 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

Similar Questions

Explore conceptually related problems

Separate the intervals of monotonicity of the following functions : f(x) = (2^(x) - 1)(2^(x) - 2)^(2)

Find the intervals in which the function f(x) = sin^(4) x + cos^(4) x AA x in [0, pi//2] is increasing and decreasing.

The least value of f(x) = sin 2x -x on [-pi//2,pi//2] is

The greatest value of the function f(x) =sin 2x -x on [-pi//2,pi//2] is

The period of the function f(x) = p|sin x| + p^(2)|cos x| + g(p) is (pi)/(2) , if p is

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

AAKASH SERIES-MAXIMA AND MINIMA -Advanced Analytical Solved Examples
  1. Find the least value of k for which the function x^(3) + kx +1 is an i...

    Text Solution

    |

  2. Find the values of a if f(x) = 2x^(x) - a e^(-x) + (2a +1) x-3 is incr...

    Text Solution

    |

  3. Separate the intervals of monotonicity of the following functions : ...

    Text Solution

    |

  4. Separate the intervals of monotonicity of the following functions : ...

    Text Solution

    |

  5. Let f(x) and g(x) be two continous functions defined from Rrarr R, suc...

    Text Solution

    |

  6. Prove that |cos alpha - cos beta| le | alpha - beta|.

    Text Solution

    |

  7. For 0 lt x lt (pi)/(2), prove that cos (sin x) gt sin (cos x).

    Text Solution

    |

  8. Examine for maxima or minima for f(x) = {(x^(2),",",x lt 0,),(5,",","x...

    Text Solution

    |

  9. f(x) = {(cos""(pix)/(2),",",x gt 0,),("x + a",",",x le 0,):}. Find the...

    Text Solution

    |

  10. Discuss the extremum of f(x) = 2x + 3x^(2//3).

    Text Solution

    |

  11. Discuss the global maxima and global minima for f(x) = tan^(-1) x - lo...

    Text Solution

    |

  12. Let f(x) = {(x^(3) - x^(2) + 10x - 5",", x le 1),(-2x + log(2)(b^(2) -...

    Text Solution

    |

  13. The maximum value of ( cos alpha1) ( cos alpha2) … ( cos alphan) under...

    Text Solution

    |

  14. Let a, b, c be positive number. If ax^(2) + (b)/(x) = c for all x gt 0...

    Text Solution

    |

  15. If f(x) = 2sin^(3) x + lambda sin^(2) x, x - (pi)/(2) lt x lt (pi)/(2)...

    Text Solution

    |

  16. Let f''(x) gt 0 AA x in R and g(x) = g(x) = 2f((x^(2))/(2)) + f(6-x^(2...

    Text Solution

    |

  17. If the equation x^(4) + 4x^(3) - 2x^(2) - 12 x + k = 0 has 4 real root...

    Text Solution

    |

  18. One corner of a rectangle of width one unit is folded over so as to re...

    Text Solution

    |

  19. Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real ro...

    Text Solution

    |

  20. Show that the function f(x) = 2x^(2) - 3(lambda + 2) x^(2) + 2 lambdax...

    Text Solution

    |