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

Options

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

Answer

A

Explanation

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.