The function f x = 2 x 3 - 3 a + b x 2 + 6 a b x has a local maximum at x = a, if

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Question: Answered & Verified by Expert

The function

f (x) = 2 x^{3} - 3 (a + b) x^{2} + 6 a b x

has a local maximum at

x = a,

if

MathematicsApplication of DerivativesJEE Main

Options:

A $a > b$
B $a < b$
C $a > 0$
D $a < 0$

Solution:

2907 Upvotes Verified Answer

The correct answer is:

a < b

f^{'} (x) = 6 (x^{2} - (a + b) x + a b)

= 6 (x - a) (x - b)

i.e.

f (x)

has local maximum at

x = a

if

a < b

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