Home
Class 12
MATHS
Show that f(x)=x^(3)-3x^(2)+4x, x in R i...

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise MISCELANEOUS EXERCISE - 6|27 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

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

Show that f(x)=x^(3)-6x^(2)+12x-18 is an increasing function on R.

If ……….., then f(x)=x^(2)-kx+20, [0,3] is strictly increasing.

Without using differentiation, prove that f(x)=ax+b , where a gt 0 is strictly increasing function AA x in R .

Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R.

Prove that the function given by f(x)=x^(3)-3x^(2)+3x-100 is increasing in R.

If f(x)=x^(3)+ax^(2)+bx+5sin^(2)x, AA x in R is an increasing function, then …………..

Find the interval in which the function f(x)=x^(4)+32x is increasing or decreasing. x in R

Find the intervals in which the function f given by f(x)=4x^(3)-6x^(2)-72x+30 is (a) Increasing (b) Decreasing.

Show that for a ge 1, f(x)=sqrt(3)sin x - cos x - 2ax + b is decreasing in R.

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. Find the in intervals in which f(x)=sin^(4)x+cos^(4)x is increasing or...

    Text Solution

    |

  2. f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is st...

    Text Solution

    |

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

    Text Solution

    |

  4. Without using differentiation, prove that f(x)=ax+b, where a gt 0 is s...

    Text Solution

    |

  5. f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which...

    Text Solution

    |

  6. Find the equation of the tangent to the curve y^(2)=16x which is paral...

    Text Solution

    |

  7. Find the equation of the normal to the curve y = 8x which is perpendic...

    Text Solution

    |

  8. Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts ortho...

    Text Solution

    |

  9. Find the equation of the tangent and normal to the curve y^(2)(a+x)=x^...

    Text Solution

    |

  10. Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) i...

    Text Solution

    |

  11. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

    Text Solution

    |

  12. A line x cos alpha + y sin alpha = P is a tangent to the curve (x^(2))...

    Text Solution

    |

  13. Find the equations of the tangent to the curve y=cos(x+y) which is par...

    Text Solution

    |

  14. Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the...

    Text Solution

    |

  15. The slope of the tangent to the curve xy+ax+by=2 at a point (1, 1) the...

    Text Solution

    |

  16. Prove that all points on the curve y^(2)=4a[x+a sin((x)/(a))] at which...

    Text Solution

    |

  17. Find the equation of the normal to the curve y=(1+x)^(y)+sin^(-1)(sin^...

    Text Solution

    |

  18. If the curves (x^(2))/(a^(2))+(y^(2))/(4)=1 and y^(3)=16x intersect at...

    Text Solution

    |

  19. Find the equations of the tangents drawn to the curve y^(2)-2x^(3)-4y+...

    Text Solution

    |

  20. Find the approximate value of each of the following : sqrt(399)

    Text Solution

    |