Home
Class 12
MATHS
Show that f(x)=cosx is decreasing functi...

Show that `f(x)=cosx` is decreasing function on `(0,pi),` increasing in `(-pi,0)` and neither increasing nor decreasing in `(-pi,pi)dot`

Text Solution

Verified by Experts

`f(x)=cos x`
Domain of `cos x is (-pi, pi).`
`Rightarrow f^{prime}(x)=-sin x`
For `x in(-pi, 0), sin x<0`
` Rightarrow-sin x>0 `
` ...
Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

Show that f(x)=cos x is a decreasing function on (0,pi), increasing in (pi,0) and neither increasing nor decreasing in (pi,pi) .

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

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

Show that f(x)=sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi) and neither increasing nor decreasing in (0,pi)

Show that f(x)=sin x is an increasing function on (-pi/2,pi/2)

Show that f(x)=tan x is an increasing function on (-pi/2,pi/2)

Show that f(x)=sin x-cos x is an increasing function on (-pi/4,pi/4)

Show that f(x)=x^(2)-x sin x is an increasing function on (0,pi/2)

Show that f(x)=log sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi).

Show that f(x)=cos(2x+pi/4) is an increasing function on (3 pi/8,7 pi/8)

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=cos^2x is decreasing function on (0,pi/2)dot

    Text Solution

    |

  2. Show that f(x)=x^2-xsinx is an increasing function on (0,pi/2)dot

    Text Solution

    |

  3. Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-...

    Text Solution

    |

  4. Show that f(x)=tan^(-1)(sinx+cosx) is decreasing function on the inter...

    Text Solution

    |

  5. Show that function f(x)=sin(2x+pi/4) is decreasing on ((3pi)/8,(5pi)/8...

    Text Solution

    |

  6. Show that f(x)=x-sinx is increasing for all x in R

    Text Solution

    |

  7. Find the value(s) for a for which f(x)=x^3-a x is an increasing functi...

    Text Solution

    |

  8. Find the intervals in which function f(x) = sin x-cos x, 0 lt x lt 2pi...

    Text Solution

    |

  9. Determine the values of x for which the function f(x)=x^2-6x+9 is incr...

    Text Solution

    |

  10. Find the intervals in which the following function are increasing or ...

    Text Solution

    |

  11. Show that f(x)=e^(1/x),x!=0 is decreasing function for all x!=0.

    Text Solution

    |

  12. Show that f(x)=e^(2x) is increasing on Rdot

    Text Solution

    |

  13. Show that f(x)=x^9+4x^7+11 is an increasing function for all x inRdot

    Text Solution

    |

  14. State when a function f(x) is said to be increasing on an interval [a ...

    Text Solution

    |

  15. Determine whether f(x)=-x//2+sinx is increasing or decreasing on (-pi/...

    Text Solution

    |

  16. Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

    Text Solution

    |

  17. Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreas...

    Text Solution

    |

  18. Prove that the function f given by f(x)=x-[x] us ubcreasubg ub (0,1)do...

    Text Solution

    |

  19. Show that the function f given by f(x)=10^x is increasing for all xdot

    Text Solution

    |

  20. Without using the derivative, show that the function f(x)=|x| is stric...

    Text Solution

    |