Home
Class 12
MATHS
Let f,g : [-1,2] to be continuous funct...

Let `f,g : [-1,2] to` be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the points and 2 be as given in the following table:

In each of the intervals (-1,0) and (0, 2) the function (f-3g) never vanishes. Then the correct statements(s) is(are) :

A

f'(x)-3g'(x)=0 has exactly three solution in `(-1,0) cup (0,2)`

B

`f'(x)-3g'(x)=0` has exactly one solution in (-1,0)

C

f'(x)-3g'(x)=0 has exactly one solution in (0, 2)

D

f'(x)-3g'(x)=0 has exactly two solutions in and exactly two solutions in (0, 2)

Text Solution

Verified by Experts

The correct Answer is:
B, C
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

Let f,g:[-1,2]rarr RR be continuous functions which are twice differentiable on the interval (-1, 2). Let the values of f and g at the points –1, 0 and 2 be as given in the following table : x=-1 x=0 x=2 f(x) 3 6 0 g(x) 0 1 -1 In each of the intervals (-1,0) and (0, 2) the function (f – 3g)'' never vanishes. Then the correct statement(s) is(are)

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

If f(x) = |x+1|(|x|+|x-1|) , then at what point(s) is the function not differentiable over the interval [-2, 2] ?

Let f: (-2, 2) rarr (-2, 2) be a continuous function such that f(x) = f(x^2) AA Χin d_f, and f(0) = 1/2 , then the value of 4f(1/4) is equal to

Let f be continuous and the function g is defined as g(x)=int_0^x(t^2int_1^t f(u)du)dt where f(1) = 3 . then the value of g' (1) +g''(1) is

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

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 and g be function continuous in [a,b] and differentiable on [a,b] .If f(a)=f(b)=0 then show that there is a point c in (a,b) such that g'(c) f(c)+f'(c)=0 .

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

Let g be the inverse function of a differentiable function f and G (x) =(1)/(g (x)). If f (4) =2 and f '(4) =(1)/(16), then the value of (G'(2))^(2) equals 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

    |