Home
Class 12
MATHS
Which of the following functions are dec...

Which of the following functions are decreasing on `(0,\ pi//2)` ? (i) `cosx` (ii) `cos2x` (iii) `tanx` (iv) `cos3x`

A

sin2x

B

tanx

C

cosx

D

cos3x

Text Solution

Verified by Experts

The correct Answer is:
C
In the interval `(0,pi/2)`, f(x) = cosx
`rArr f^(')(x)=-sinx`
Which gives `f^(')(x) lt0` in `(0,pi/2)`
Hence, f(x) = cosx is decreasing in `(0,pi/2)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

Similar Questions

Explore conceptually related problems

Which of the following functions are decreasing on (0,pi/2)?(i)cos x(ii)cos2x (iii) tan x (iv) cos3x

which of the following functinon are strictly decreasing on (0,pi/2) a) cos x b) cos2x c) cos3x d) tanx

Which of the following functions are strictly decreasing on [0,(pi)/(2)] (A) (B) cos 2x (C) tan x

Show that f(x)=cos^(2)x is a decreasing function on (0,pi/2)

(i) cos3x=cos2x (ii) cos5x=sin3x (iii) cosmx=sinnx

Which of the following functions are periodic - (1) sin x+cos x(2)cos x+{(x)/(pi)}(3)cos pi x+{2x}(4)ln{x}+sin2x

Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5sec x+4 cos x (iv) cosec x (v) 3 cot x+5 cosec x (vi) 5sinx-6cosx+7 (vii) 2tanx-7secx

Find the periods of the following functions, if periodic : (i) | cos x | (ii) 2 "cos" (1)/(3)(x - pi)

Differentiate the following functions with respect to x:(i)log(cos x^(2)) (ii) cos(log x)^(2)

Sketch the graphs of the following function: (i) y="cos"(x)/(2) (ii) y=3 cos 2x

NCERT EXEMPLAR-APPLICATION OF DERIVATIVES-Application Of Derivatives
  1. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

    Text Solution

    |

  2. 24. Find the intervals in which the following function is (a) increasi...

    Text Solution

    |

  3. The function f:R rarr R be defined by f(x)=2x+cosx then f

    Text Solution

    |

  4. If y=x(x-3)^(2) decreases for the values of x given by

    Text Solution

    |

  5. The function f(x) =4sin^(3)x-6sin^(2)x +12 sinx + 100 is strictly

    Text Solution

    |

  6. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

    Text Solution

    |

  7. The function f(x)= tan x - x

    Text Solution

    |

  8. If x is real, then the minimum value of the expression x^2-8x+17 is

    Text Solution

    |

  9. Show that the least value of the function f(x)=x^3-18 x^2+96 x in the ...

    Text Solution

    |

  10. Show that the least value of the function f(x)=2x^3-3x^2-12x+1 on [-2,...

    Text Solution

    |

  11. Show that The maximum value of sinx. cosx in R is 1/2

    Text Solution

    |

  12. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is

    Text Solution

    |

  13. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

    Text Solution

    |

  14. The function f(x)=x^(x) has a stationary point at

    Text Solution

    |

  15. Show that the maximum value of (1/x)^x is e^(1//e) .

    Text Solution

    |

  16. The curves y=4x^(2)+2x-8 and y=x^(3)-x+13 touch each other at the poin...

    Text Solution

    |

  17. The equation of normal to the curve y=tanx at (0,0) is ………………..

    Text Solution

    |

  18. Find the values of ' a ' for which the function f(x)=sinx-a x+4 is inc...

    Text Solution

    |

  19. The function f(x)=(2x^2-1)/x^4, x gt 0decreases in the interval

    Text Solution

    |

  20. The least function value of function f(x) =ax + b/x (where, a gt 0, b ...

    Text Solution

    |