Home
Class 12
MATHS
Prove that funciton given by (i) f(x...

Prove that funciton given by
(i) `f(x)=x^(2)` is
(a) Strictly increasing in ` x in (0,oo)`
(b) Strictly decreasing in ` x in (-oo,0)`
(ii) `f(x)=tan x ` is strictly increasing in ` x in (npi-(pi)/(2),n pi+(pi)/(2))`, where ` n in I`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-B( Objective Type Questions ( One option is correct ))|31 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-J (Aakash Challengers Questions )|8 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

Prove that function given by f(x)=sin x is (i) Strictly increasing in (-(pi)/(2),(pi)/(2)) (ii) Strictly decreasing in ((pi)/(2),(3pi)/(2))

Find the interval in which the function f given by f(x)=x^(2)-2x+3 is (a) Strictly increasing (b) Strictly decreasing

Without using the derivative, show that the function f(x)=|x| is (a) strictly increasing in (0,\ oo) (b) strictly decreasing in (-oo,\ 0)

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

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

Find the intervals in which the function f given by f(x)=x^2-4x+6 is (a) strictly increasing (b) strictly decreasing

Find the intervals in which the function f given by f(x)=2x^2-3x is(a) strictly increasing (b) strictly decreasing

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Find the intervals in which the function f given by f(x)=2x^3-3x^2-36 x+7 is (a) strictly increasing (b) strictly decreasing

Find the intervals in which f(x)=4x^(3)-45x^(2)+168x-16 is (i) Strictly increasing (ii) Strictly decreasing

AAKASH INSTITUTE ENGLISH-APPLICATION OF DERIVATIVES-TRY YOURSELF
  1. Show that f(x)=[x], ([] implies greatest integer function ) is increas...

    Text Solution

    |

  2. Show that f(x)=1/x is a decreasing function on (0,\ oo) .

    Text Solution

    |

  3. Prove that funciton given by (i) f(x)=x^(2) is (a) Strictly i...

    Text Solution

    |

  4. Find the interval in which the function f given by f(x)=x^(2)-2x+3 is ...

    Text Solution

    |

  5. Prove that f(x)=tan ^(-1)(sin x + cos x ),x gt 0 f(0,pi/4) is incre...

    Text Solution

    |

  6. Find the slope of tangent to curve y=x+2log x at x=1.

    Text Solution

    |

  7. Distance between the points on the curve 4x^2 + 9y^2 = 1, where tangen...

    Text Solution

    |

  8. Find the point at which the tangent to the curve y=(3)/(5)x^(5)-(5)/(3...

    Text Solution

    |

  9. Find pints on the curve (x^2)/9+(y^2)/(16)=1 at which the tangents ...

    Text Solution

    |

  10. Find the equation of a line having slope is equal to 2,which touching ...

    Text Solution

    |

  11. Find the equation of the tangent to the curve y=(x-7)/((x-2)(x-3) at ...

    Text Solution

    |

  12. Find the equations of the tangent and the normal to the curve x^(2/...

    Text Solution

    |

  13. Find the equation of tangent to the curve given by x=2 sin^(3)t ,y=2 ...

    Text Solution

    |

  14. The normal to the curve x=a(cos theta + theta sin theta), y=a(sin thet...

    Text Solution

    |

  15. Prove that the segment of tangent to xy=c^(2) intercepted between the...

    Text Solution

    |

  16. Find the equations of tangent to the curve y=x^(4) which are drawn fro...

    Text Solution

    |

  17. Find the approximate value of sqrt(36.6.)

    Text Solution

    |

  18. If the radius of a sphere is measured as 9cm with an error of 0.03 cm,...

    Text Solution

    |

  19. Find the approximate value of sin((5pi)/(16)) .

    Text Solution

    |

  20. Find the maximum and minimum value if any , of the function f given by...

    Text Solution

    |