Application of DerivativeHard
Question
The function f(x) = x3 - 6x2 + ax + b satisfy the conditions of Rolle′s theorem on [1, 3]. Which of these are correct ?
Options
A.a =11, b ∈ R
B.a = 11, b = - 6
C.a = - 11, b = 6
D.a = - 11, b ∈ R
Solution
f(x) = x3 - 6x2 + ax + b
f(x) satisfies condition in Rolle′s theorem on [1, 3]
f(1) = f(3)
⇒ 1 - 6 + a + b = 27 - 54 + 3a + b
2a = 22
a = 11
and b ∈ R
f(x) satisfies condition in Rolle′s theorem on [1, 3]
f(1) = f(3)
⇒ 1 - 6 + a + b = 27 - 54 + 3a + b
2a = 22
a = 11
and b ∈ R
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