Application of DerivativeHard
Question
If f(x) = (x - 4) (x - 5) (x - 6) (x - 7) then,
Options
A.f′(x) = 0 has four roots.
B.three roots of f′(x) = 0 lie in (4, 5) ∪ (5, 6) ∪ (6, 7)
C.the equation f′(x) = 0 has only one real root.
D.three roots of f′(x) = 0 lie in (3, 4) ∪ (4, 5) ∪ (5, 6).
Solution
f(4) = f(5) = f(6) = f(7) = 0
By Rolle′s theorem on interval
[4, 5], [5, 6], [6, 7] we have
f′(x) = 0 for at least once in each intervals (4, 5), (5, 6), (6, 7).
By Rolle′s theorem on interval
[4, 5], [5, 6], [6, 7] we have
f′(x) = 0 for at least once in each intervals (4, 5), (5, 6), (6, 7).
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