Home
Class 12
MATHS
Let f(x) be a function such that its der...

Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function `phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2)`A. If Rolle's theorem is applicable to `phi(x)` on, [a,b], answer following questions.
If there exists some unmber c(a lt c lt b) such that `phi'(c)=0 and f(b)=f(a)+(b-a)f'(a)+lambda(b-a)^(2)f''(c)`, then `lambda` is

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) such that f(a)/a=f(b)/b . Prove that there exist x_0 in (a, b) such that f'(x_0 ) = f(x_0)/x_0

If the function f(x) and g(x) are continuous in [a, b] and differentiable in (a, b), then the f(a) f (b) equation |(f(a),f(b)),(g(a),g(b))|=(b-a)|(f(a),f'(x)),(g(a),g'(x))| has, in the interval [a,b] :

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 .

If f(x)={x ,xlt=1,x^2+b x+c ,x >1' 'find b and c if function is continuous and differentiable at x=1

Let f is continuous on [a, b] and differentiable on (a,b)s.t.t^2(a)-t^2(b)=a^2-b^2. Show that ... f(x) f prime (x) = x has atleast one root in (a, b).

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

If the functions f(x) and g(x) are continuous on [a,b] and differentiable on (a,b) then in the interval (a,b) the equation |{:(f'(x),f(a)),(g'(x),g(a)):}|=(1)/(a-b)=|{:(f(a),f(b)),(g(a),g(b)):}|

If f(x) is continuous in [a , b] and differentiable in (a,b), then prove that there exists at least one c in (a , b) such that (f^(prime)(c))/(3c^2)=(f(b)-f(a))/(b^3-a^3)

If f(x) is continuous in [a , b] and differentiable in (a,b), then prove that there exists at least one c in (a , b) such that (f^(prime)(c))/(3c^2)=(f(b)-f(a))/(b^3-a^3)

Let a , b , c be three real numbers such that a < b < c . f(x) is continuous in [a , c] and differentiable in (a , c) Also, f^(prime)(x) is strictly increasing in (a , c) Prove that (b-c)f(a)+(c-a)f(b)+(a-b)f(c)<0.

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Let f(x)= cosec 2x + cosec^(2)2 x+ cosec^(2)3 x+........+ cosec^(2)n ...

    Text Solution

    |

  2. Let ' P ' a point on the line y=3x and Q lies on 2y+x=2 and the mid-po...

    Text Solution

    |

  3. Let f(x) be a function such that its derovative f'(x) is continuous in...

    Text Solution

    |

  4. The number of positive integral solutions of, (x^2(3x-4)^3(x-2)^4)/((x...

    Text Solution

    |

  5. Let f(x)=e^(2x) and b=a+hdot If there exists a real number theta in (0...

    Text Solution

    |

  6. If 3A=[(-1,-2,-2),(2,1,-2),(x,-2,y)] such that A A^T=I, then which of ...

    Text Solution

    |

  7. Solve for x:log(2)(sin""(x)/(2))lt-1

    Text Solution

    |

  8. Let f(x)=x^4-6x^3+12 x^2-8x+3. If Rolles theorem is applicable to varp...

    Text Solution

    |

  9. The equation "sin"^(4) x - (k +2)"sin"^(2) x - (k + 3) = 0 possesses a...

    Text Solution

    |

  10. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  11. xdotC(21)+ydotC(22)+zdotC(23) is (a)0 (b) delta (c) -delta (d) Non...

    Text Solution

    |

  12. The number of real solution of the equation. sin(e^(x))=5^(x)+5^(-x) ...

    Text Solution

    |

  13. qdotM(12)+ydotM(22)+mdotM(32)= (a) 0 (b) triangle (c) -triangle (d...

    Text Solution

    |

  14. The left hand derivative of f(x)=[x]sin(pix) at x = k, k in Z, is

    Text Solution

    |

  15. If 4a^2+c^2=b^2-4a c , then the variable line a x+b y+c=0 always passe...

    Text Solution

    |

  16. If f(x)={{:([x]+sqrt({x})",", xlt1),((1)/([x]+{x}^(2))",",xge1):}, the...

    Text Solution

    |

  17. pdotC(21)+qdotC(22)+rdotC(23)= (a) 0 (b) triangle (c) -triangle (d...

    Text Solution

    |

  18. Let A" "=" "{9," "10 ," "11 ," "12 ," "13} and let f" ":" "A ->N be de...

    Text Solution

    |

  19. If (0,1),(1,1)a n d(1,0) be the middle points of the sides of a triang...

    Text Solution

    |

  20. The quadratic equation whose root:s are sec^2 alpha and cosec^2 alpha...

    Text Solution

    |