Home
Class 12
MATHS
Statement -1 The maximum value of f(x)=1...

Statement -1 The maximum value of `f(x)=1/(3x^4+8x^3-18x^2+60) "is"1/(53)`
Statement -2 : The function g(x) =`1/(f(x))` attains its minimum value at x=1 and x=-3

A

Statement-1 is True, Statement-2 is True,Statement -2 is a correct explanation for Statement -1

B

Statement -1 True ,Statement -2 is True ,Stament -2 is not a correct explanation for Statement -!

C

Statement -1 is True Statement -2 is False

D

Statement -1 is Flase,Statement -2 is True

Text Solution

Verified by Experts

The correct Answer is:
A

We have
`g(x)=1/f(x)=3x^4+8x^3-18x^2+60`
`rArr g'(x)=12x^3+24x^2-36x=12x(x+3)(x-1)`
The signs g'(x) for different values of x are as shown below
So , g(x) attains local minima at x=-3 and x=1
Values of g(x) at these jpoints are
g(-3)=-75 and g(1) =53
So maximum value of f(x)=`1/(g(1))=53`
Hence both the statements are true and statement -2 is a correction explanation for statements -1.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Exercise|50 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|72 Videos
  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos
  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

Find the maximum value of f(x)=(40)/(3x^(4)+8x^(3)-18x^(2)+60)

The absolute maximum value of f(x) = (5)/(3x^(4) + 8x^(3) -18x^(2) + 60)

Knowledge Check

  • Maximum value of f(x)= (x-2)^(2) . (x-3) +1 is

    A
    `0`
    B
    `1`
    C
    `2`
    D
    `3`
  • The maximum and minimum values for the funtion f(x)= 3x^4-4x^3 on [-1,2] are

    A
    7,0
    B
    0,-7
    C
    16,-1
    D
    `-7,16`
  • The maximum value of the function f(x)=(1+x)^(0.3)/(1+x^(0.3)) in [0,1] is

    A
    1
    B
    `2^(0.7)`
    C
    `2^(-0.7)`
    D
    `2^(0.3)`
  • Similar Questions

    Explore conceptually related problems

    The maximum and minimum values of f(x)=(x-1)(x-2)(x-3) are

    The maximum value of the function f(x)=(x^(4)-x^(2))/(x^(6)+2x^(3)-1) where x>1 is equal to:

    The maximum value of the function f(x)=[x(x-1)+1]^((1)/(3)) ; x in [0,1] is

    Find the maxima and minimum value of the function y = 40/(3x^(4)+ 8x^(3)- 18x^(2) +60 .

    The minimum value of the function f(x) = 2|x - 1| + |x - 2| is