Apply the generalized Rolle's theorem to f(x) = x(x - 1)(x - 3) over [0,3].

musicbachv7

musicbachv7

Answered question

2022-08-02

Apply the generalized Rolle's theorem to f(x) = x(x - 1)(x - 3) over [0,3].

Answer & Explanation

Holly Crane

Holly Crane

Beginner2022-08-03Added 14 answers

f(0)=f(3)=0
so
f'(x) = (x-1)(x-3) + x(x-3) + x(x-1)
let f'(c) = (c-1)(c-3) + c(c-3) + c(c-1) = 0
c 2 3 c c + 3 + c 2 3 c + c 2 c = 3 c 2 8 c + 3 = 0
с = 8 ± 64 3 4 3 2 3 = 4 ± 7 3

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