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Question
Choose the correct option from the given alternatives :
If the function f(x) = ax3 + bx2 + 11x – 6 satisfies conditions of Rolle's theoreem in [1, 3] and `f'(2 + 1/sqrt(3))` = 0, then values of a and b are respectively
Options
1, – 6
– 2, 1
– 1, – 6
– 1, 6
Solution
1, – 6
[Hint : f(x) = ax3 + bx2 + 11x – 6 satisfies the conditions of Rolle's theorem in [1, 3]
∴ f(1) = f(3)
∴ a(1)3 + b(1)2 + 11(1) – 6 = a3 + b(3)2 + 11(3) - 6
∴ a + b + 11 = 27a + 9b + 33
∴ 26a + 8b = – 22
∴ 13a + 4b = – 11
Only a = 1, b = – 6 satisfy this equation].
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