Home
Class 11
MATHS
Show that f(x) = cos^(2) x is strictly d...

Show that `f(x) = cos^(2) x` is strictly decreasing on `(0, pi//2)`.

Text Solution

Verified by Experts

The correct Answer is:
cosx
Promotional Banner

Topper's Solved these Questions

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise SYNOPSIS|22 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-I|31 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-7.2 LONG ANSWER QUESTIONS)|3 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (PRACTICE SHEET )(ADVANCED)) (INTEGER TYPE QUESTIONS)|3 Videos

Similar Questions

Explore conceptually related problems

Show that f(x)=|x| is strictly decreasing on (-oo, 0) and strictly increasing on (0, oo) .

Without using the derivative, show that The function f(x) = 5-7x is strictly decreasing on R

Without using the derivative, show that The function f(x) = ((1)/(2))^(x) is strictly decreasing on R

f(x) = Cos^(-1) x is decreasing in

Prove that the function log sin x is strictly increasing (0,pi/2) and strictly decreasing on (pi/2,pi)

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).

Show that the function f given by f(x) = tan^(-1)(sin x + cos x), x gt 0 is always an strictly increasing functions in (0, (pi)/(4))

Show that the function f(x) = sin x defined on R is neither increasing nor decreasing on (0, pi) .

Let f(x)=sinx-cosx be defined on [0,2pi] . Determine the intervals in which f(x) is strictly decreasing and strictly increasing.

AAKASH SERIES-MAXIMA & MINIMA-ADDITIONAL EXERCISE
  1. Show that f(x) = cos^(2) x is strictly decreasing on (0, pi//2).

    Text Solution

    |

  2. Give an example of a trigonometric function which is Strictly increa...

    Text Solution

    |

  3. Prove that the function log sin x is strictly increasing (0,pi/2) and ...

    Text Solution

    |

  4. Show that the function f given by f(x) = x^(3)-3x^(2)+4x,x in R is i...

    Text Solution

    |

  5. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  6. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  7. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  8. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  9. If f(x)=x^3+ax^2+bx+5sin^2x increase for all x in R show that a^2-3b+1...

    Text Solution

    |

  10. Show that x^(1//x) is increasing in (0,e) and decreasing in (e,oo). He...

    Text Solution

    |

  11. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  12. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  13. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  14. Find the points of local maximum or local minimum for the following ...

    Text Solution

    |

  15. Find the points of local maximum or local minimum for the following ...

    Text Solution

    |

  16. The minimum value of a^2sec^2theta +b^2 cosec^2 theta is

    Text Solution

    |

  17. If y = a log|x| + bx^(2) + x has extreme values at x = 2 and x = -4/3 ...

    Text Solution

    |

  18. If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

    Text Solution

    |

  19. A cubic function of x ahs maximum 10 and minimum -5//2, when x=-3 and ...

    Text Solution

    |

  20. Find the triangle of the greatest area among the right triangles of a ...

    Text Solution

    |