If f x = 3 x 3 - 9 x 2 - 27 x + 15 , then the maximum value of f x is ________

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Question: Answered & Verified by Expert

If

f (x) = 3 x^{3} - 9 x^{2} - 27 x + 15,

then the maximum value of

f (x)

is ________

MathematicsApplication of DerivativesMHT CETMHT CET 2019 (02 May Shift 1)

Options:

A $- 66$
B $30$
C $- 30$
D $66$

Solution:

1944 Upvotes Verified Answer

The correct answer is:

30

If

f (x) = 3 x^{3} - 9 x^{2} - 27 x + 15

f' (x) = 9 (x^{2} - 2 x - 3) = 9 (x - 3) (x + 1)

f (x)

maximum at

x = - 1 \Rightarrow f (- 1) = - 3 - 9 + 27 + 15 = 30

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