Explanation Given: f ( x ) = x 4 − 8 x 2 − 128 First of all, let us substitute the value of c = 4 in the given function, f ( 4 ) = 4 4 − 8 ( 4 ) 4 − 128 = 256 − 128 − 128 = 0 Form this it is clear that c = 4 is a root of the given function, f ( x ) = x 4 − 8 x 2 − 128 . Now, we proceed with contradiction rule to prove that c = 4 is largest root of the function. Let us suppose that there exists a real root, say x = a; where a > 4. According to Rolle’s Theorem there exists a real number c ∈ ( 4 , a ) such that f’(c) = 0 since the given polynomial function is continuous and differentiable for all real values of x

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Chapter 4.2, Problem 68E

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To prove that f(x)=x4−8x2−128 has a largest rootof c = 4.

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Chapter 4.2, Problem 67E

Chapter 4.2, Problem 69E

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Chapter 4 Solutions

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To prove that f ( x ) = x 4 − 8 x 2 − 128 has a largest rootof c = 4.

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