Application of DerivativeHard
Question
If the function f(x) = x3 - 6x2 + ax + b defined on [1, 3], satisfies the rolle′s theorem for c = 
, then-
, then-Options
A.a = 11, b = 6
B.a = -11, b = 6
C.a = 11, b ∈ R
D.None of these
Solution
f(x) = x3 - 6x2 + ax + b
x ∈ [1, 3]
satisfies Rolle′s theorem
f(1) = 1 - 6 + a + b
f(1) = a + b - 5
f(3) = 3a + b - 27
f(1) = f(3)
a + b - 5 = 3a + b - 27
22 = 2a
a = 11 and b ∈ R
a = 11 and b ∈ R
x ∈ [1, 3]
satisfies Rolle′s theorem
f(1) = 1 - 6 + a + b
f(1) = a + b - 5
f(3) = 3a + b - 27
f(1) = f(3)
a + b - 5 = 3a + b - 27
22 = 2a
a = 11 and b ∈ R
a = 11 and b ∈ R
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