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Question

If the function f(x)= x³-3ax²+b is strictly increasing derivative for x > 0, then which of the following is always true?

A

a can take any real value

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B

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C

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D

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Solution

The correct option is D
f(x) = x³ -3ax² + b

f'(x) = 3x² - 6ax

for f(x) to be increasing f'(x) > 0.

3x² - 6ax > 0

3x (x - 2a) > 0

(x - 2a) > 0 [There fore x > 0]

x > 2a

So, a ≥0

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