Home
Class 12
MATHS
Let g(x)=f(logx)+f(2-logx)a n df''(x)<0A...

Let `g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot` Then find the interval in which `g(x)` increases.

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 g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) increases in (a) (1/2,2) (b) (4/3,2) (c) (0,2) (d) (0,4/3)

Let g(x)=2f(x/2)+f(x) and f''(x)lt0 " in "0lexle1 , then g(x)

Let g(x)=e^(f(x)) and f(x+1)=x+f(x) AA x in R . If n in I^(+)", then"(g'(n+(1)/(2)))/(g(n+(1)/(2)))-(g'((1)/(2)))/(g((1)/(2)))=

Which of the following function is non-differentiable in domain? f(x)=(x-2)/(x^2+3) (b) f(x)=log|x| f(x)=x^3logx (d) f(x)=(x-3)^(3/5)

Let f(x)=tanx a n d g(f(x))=f(x-pi/4), where f(x)a n dg(x) are real valued functions. Prove that f(g(x))="tan ((x-1)/(x+1))dot

Let f(x)gt0 for all x and f'(x) exists for all x. If f is the inverse function of h and h'(x)=(1)/(1+logx) . Then f'(x) will be

Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)(0)=3. Find f^(prime)(5)dot

Let f(x) be defined on [-2,2] and is given by f(x)={(-1, -2lexlt0),(x-1, 0lexle2):} and g(x)=f(|x|)+|f(x)|, then find g(x).

"Let "g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|, where c is constant, then find lim_(xrarr0) (g(x))/(x).

IF f(x)= log_x(logx) then the value of f'(e) is

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

    Text Solution

    |

  2. Determine the local maxima and local minima of f(x)=(x+1)^2(x-1)^3 is

    Text Solution

    |

  3. Let g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot Then find the i...

    Text Solution

    |

  4. Prove that The maximum value of (sqrt(-3+4x-x^2)+4)^2+(x-5)^2(w h e r ...

    Text Solution

    |

  5. Find the points of inflection for (a)f(x)=sinx (b)f(x)=3x^4-4x^3

    Text Solution

    |

  6. Statement 1: If both functions f(t)a n dg(t) are continuous on the clo...

    Text Solution

    |

  7. Discuss monotonocity of y=f(x) which is griven by x=1/(1+t^2) and y=1...

    Text Solution

    |

  8. Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2...

    Text Solution

    |

  9. Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decr...

    Text Solution

    |

  10. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

    Text Solution

    |

  11. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

    Text Solution

    |

  12. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

    Text Solution

    |

  13. Discuss the monotonocity of function f(x)=2log|x-1|-x^2+2x+3.

    Text Solution

    |

  14. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  15. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

  16. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

    Text Solution

    |

  17. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

  18. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

    Text Solution

    |

  19. Separate the intervals of monotonocity for the function f(x)=((log)e x...

    Text Solution

    |

  20. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

    Text Solution

    |