Suppose f x is a polynomial of degree four having critical points at - 1 , 0 , 1 . If T = x ∈ R | f x = f 0 , then the sum of squares of all the elements of T is :

Question

Suppose f x is a polynomial of degree four having critical points at - 1 , 0 , 1 . If T = x &#8712; R | f x = f 0 , then the sum of squares of all the elements of T is :

Quantrex Academy · Accepted Answer

Correct answer: A. 4

f ' x = k . x x + 1 x - 1 = k x 3 - x Integrating both sides with respect to x , we get f x = k &#160; x 4 4 - x 2 2 + c &#8658; f 0 = c &#8757; &#160; &#160; f x = f 0 &#8658; k x 4 - 2 x 2 4 + c = c &#8658; x 2 x 2 - 2 = 0 &#8658; x = 0 , &#160; 2 , &#160; - 2 &#8658; T = 0 , &#160; 2 , &#160; - 2 Thus, sum of squares of all the elements of T is 0 2 + 2 2 + - 2 2 = 4 .

Suppose f x is a polynomial of degree four having critical points at - 1 , 0 , 1 . If T = x ∈ R | f x = f 0 , then the sum of squares of all the elements of T is :

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More from Application of Derivatives

Suppose f x is a polynomial of degree four having critical points at - 1 , 0 , 1 . If T = x &#8712; R | f x = f 0 , then the sum of squares of all the elements of T is :

Options

Correct answer

Step-by-step solution

More from Application of Derivatives

Suppose f x is a polynomial of degree four having critical points at - 1 , 0 , 1 . If T = x ∈ R | f x = f 0 , then the sum of squares of all the elements of T is :