Home
Class 12
MATHS
If f:R is a differentiable fucntion suc...

If f:R is a differentiable fucntion such that f(x) `gt` 2f(x) for all x `in` R and f(0) =1 then

A

f(x) is decreasing in `(0,oo)`

B

`f'(x) lt e^(2x)" in "(0,oo)`

C

f(x) is increasing in `(0,oo)`

D

`f(x) gt e^(2x)" in "(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos
  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

If f:R to R is continous such that f(x) -f(x/2)=(4x^(2))/3 for all xinR and f(0)=0, find the value of f(3/2) .

If f(x) is a continuous function such that f(x) gt 0 for all x gt 0 and (f(x))^(2020)=1+int_(0)^(x) f(t) dt , then the value of {f(2020)}^(2019) is equal to

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. Let f,g : [-1,2] to be continuous functions which are twice different...

    Text Solution

    |

  2. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

    Text Solution

    |

  3. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

    Text Solution

    |

  4. The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is ver...

    Text Solution

    |

  5. On the ellipse 4x^2+9y^2=1, the points at which the tangents are paral...

    Text Solution

    |

  6. If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >...

    Text Solution

    |

  7. If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...

    Text Solution

    |

  8. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  9. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  10. If f(x)=xe^(x(1-x)), then f'(x) is

    Text Solution

    |

  11. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  12. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

    Text Solution

    |

  13. The function f(x)=(log (pi+x))/(log (e+x))," is "

    Text Solution

    |

  14. Let fa n dg be increasing and decreasing functions, respectively, from...

    Text Solution

    |

  15. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

    Text Solution

    |

  16. Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h ...

    Text Solution

    |

  17. Let f(X) be a polynomila of degree four having extreme values at x =1 ...

    Text Solution

    |

  18. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  19. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  20. The total number of local maxima and local minima of the function f...

    Text Solution

    |