Home
Class 12
MATHS
If f(x)<0,\ x in (a , b) then at the...

If `f(x)<0,\ x in (a , b)` then at the point `C(c ,\ f(c))` on `y=f(x)` for which`F(c)` is a maximum, `f^(prime)(c)` is given by a.`f^(prime)(c)=(f(b)-f(a))/(b-1)` b. `\ f^(prime)(c)=(f(b)-f(a))/(a-b)` c.`f^(prime)(c)=(2(f(b)-f(a)))/(b-a)` d. `f^(prime)(c)=0`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos
  • LIMITS AND DERIVATIVES

    BANSAL|Exercise All Questions|436 Videos

Similar Questions

Explore conceptually related problems

If int f(x)dx=F(x),f(x) is a continuous function,then int(f(x))/(F(x))dx equals

If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x) , then f(x) is, (given f(0) = 0)

If y=f(x) satisfy (x.f(x))^(99)+(x.f(x))^(98)+...+(x.f(x))+1=0

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .

A function f satisfies the condition f(x)=f'(x)+f''(x)+f''(x)+…, where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

If f:R rarr R such that f(x)=(4^(x))/(4^(x)+2) for all x in R then (A)f(x)=f(1-x)(B)f(x)+f(1-x)=0(C)f(x)+f(1-x)=1(D)f(x)+f(x-1)=1

Given F(x)=f(x)phi(x) and f'(x)phi'(x)=c then prove that F''(x)/F(x)=(f'')/f+(phi'')/phi+2c

The function f(x) satisfies the equation f(x+1)+f(x-1)=sqrt(3)f(x) .then the period of f(x) is

BANSAL-INTEGRALS-All Questions
  1. Evaluate : int(0)^(pi//2) sin x dx

    Text Solution

    |

  2. For every function f (x) which is twice differentiable , these will be...

    Text Solution

    |

  3. If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x...

    Text Solution

    |

  4. Find the value of (5050int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^...

    Text Solution

    |

  5. (lim)(x->4)(int2sec^2\ f(t)dt)/(x^2-(pi^2)/(16)) equals a.8/pif(2) b. ...

    Text Solution

    |

  6. int(-1)^1(dx)/(1+x^2)

    Text Solution

    |

  7. int0^1(dx)/(1-x^2)\

    Text Solution

    |

  8. int2^3(dx)/(1-x^2)

    Text Solution

    |

  9. int1^2(dx)/(x\ sqrt(x^2-1))

    Text Solution

    |

  10. Let f be a non-negative function defined on the interval [0,1]dot If i...

    Text Solution

    |

  11. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

    Text Solution

    |

  12. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  13. The value of (lim)(x->0)1/(x^3)int0^x(t ln(1+t))/(t^4+4)dt is a.0 b. 1...

    Text Solution

    |

  14. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

    Text Solution

    |

  15. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  16. For any real number x ,l e t[x] denote the largest integer less than o...

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

  18. The value of the integral int(pi//2)^(pi//2)(x^2ln(pi+x)/(pi-x))cos...

    Text Solution

    |

  19. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  20. Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0^1(cosx)/(sqrt(x))dx Then w...

    Text Solution

    |