Home
Class 12
MATHS
Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3si...

Let `g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot` Then prove that `g` is increasing whenever f is increasing.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h is increasing whenever f is increasing (b) h is increasing whenever f is decreasing (c) h is decreasing whenever f is decreasing (d) nothing can be said in general

Prove that f(x)=x-sinx is an increasing function.

If 2f(x) + 3f(-x) = 15 - 4x, then prove that f(x) = 3 + 4x.

Let g(x)=f(x)+f(1-x) and f '' (x) gt 0 AA x in (0, 1) . Find the intervals of increase and decrease of g(x) -

let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number x. Prove that h(x) is increasing or decreasing according as f(x) is increasing or decreasing.

If f(x)=x^(2)andg(x)=sqrtx , then prove that g(f(4)) = 4.

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? (a) [f(x)]^(g(x)) is always increasing (b) [f(x)]^(g(x)) is decreasing, when f(x) 1,t h e n[f(x)]^(g(x)) is increasing.

Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where p>0 , then prove f(x) is periodic.

If f(x)=log_(3)xandg(x)=x^(2) , then prove that f(g(3)) = 2.

Let f(x)=2x-sinx and g(x) = 3sqrtx . Then

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^...

    Text Solution

    |

  2. Given g(x)=(x+2)/(x-1) and the line 3x+y-10=0. Then the line is tangen...

    Text Solution

    |

  3. Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot Then prov...

    Text Solution

    |

  4. Let f be a continuous, differentiable, and bijective function. If the ...

    Text Solution

    |

  5. Find the intervals of decrease and increase for the function f(x)=cos(...

    Text Solution

    |

  6. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

    Text Solution

    |

  7. Find the interval of monotonocity of the function f(x)=|x-1|/x^2dot

    Text Solution

    |

  8. A continuous and differentiable function y=f(x) is such that its graph...

    Text Solution

    |

  9. Find the intervals in which the function f given by f(x)=(4sinx-2x-xc...

    Text Solution

    |

  10. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |

  11. Prove that the following functions are strictly increasing: f(x)=cot^(...

    Text Solution

    |

  12. The radius of the base of a cone is increasing at the rate of 3 cm/min...

    Text Solution

    |

  13. Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

    Text Solution

    |

  14. Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,...

    Text Solution

    |

  15. Find the number of solutions of the equation 3tanx+x^3=2 when x in...

    Text Solution

    |

  16. If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have a....

    Text Solution

    |

  17. Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of...

    Text Solution

    |

  18. If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...

    Text Solution

    |

  19. Show that tan^(-1)x > x/(1+(x^2)/3)ifx in (0,oo)dot

    Text Solution

    |

  20. Consider the function f(x)={xsinpi/x ,forx >0 ,forx=0 The number of ...

    Text Solution

    |