Home
Class 12
MATHS
Let f(x) be a polynomial of degree four ...

Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2. IF `lim_(xto0) [1+(f(x))/x^2]=3`, then f(2) is equal to

A

-8

B

-4

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos
  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise CRITICAL THINKING|129 Videos
  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos
  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2. If lim_(x to 0)(1+(f(x))/(x^(2)))=3, then f(2) is equal to

Let f(x) be a polynomial of degree four having extreme values at x""=""1 and x""=""2 . If (lim)_(xvec0)[1+(f(x))/(x^2)]=3 , then f(2) is equal to : (1) -8 (2) -4 (3) 0 (4) 4

Let p (x) be a real polynomial of degree 4 having extreme values x=1 and x=2.if lim_(xrarr0) (p(x))/(x^2)=1 , then p(4) is equal to

If p(x) is a polynomial of degree 6 with coefficient of x^6 equal to 1 . If extreme value occur at x=1 and x=-1 , lim_(xrarro)(f(x)/x^3)=1 then 5f(2)=

Let f(x) be a polynomial of degree 4 such that f(1)=1,f(2)=2,f(3)=3,f(4)=4 and lim_(x rarr oo)(xf(x))/(x^(5)+1)=1 then value of f(6) is

Let f(x) be a polynomial of least degree such that lim_(x rarr0)(1+(x^(4)+f(x^(2)))/(x^(3)))^(1/x)=e^(3), then write the value of f(3)

Let f(x) be a polynomial of degree 4 on R such that lim_(x rarr1)(f(x))/((x-1)^(2))=1 If f'(0)=-6 and f'(2)=6, then find global maximum value of f(x) in [(1)/(2),2]

f:RtoR such that f(2)=5 and f'(2)=10 then lim_(xto0) ((f(2+x))/(f(2)))^(1//x) is equal to:

Let f(x) be a polynomial of degree 6 divisible by x^(3) and having a point of extremum at x = 2 . If f'(x) is divisible by 1 + x^(2) , then find the value of (3f(2))/(f(1)) .

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING
  1. Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . ...

    Text Solution

    |

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

    Text Solution

    |

  3. Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....

    Text Solution

    |

  4. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

    Text Solution

    |

  5. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  6. If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} an...

    Text Solution

    |

  7. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  8. Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f ...

    Text Solution

    |

  9. Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only re...

    Text Solution

    |

  10. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  11. The points on the curve y=12x-x^3 at which the gradient is zero are

    Text Solution

    |

  12. The displacement of a particle at time t is x, where x=t^4-kt^3. IF th...

    Text Solution

    |

  13. If f(x) satifies of conditiohns of Rolle's theorem in [1,2] and f(x) i...

    Text Solution

    |

  14. IF f(x)=x,-1lexle1, then function f(x) is

    Text Solution

    |

  15. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

    Text Solution

    |

  16. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

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

    Text Solution

    |

  18. if Agt0,Bgt0 and A+B=pi/3 then the maximum value of tanA.tanB is (A) 1...

    Text Solution

    |

  19. A wire of length 2 units is cut into two parts which are bent respe...

    Text Solution

    |

  20. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

    Text Solution

    |