JEE Advance - Mathematics (2009 - Paper 2 Offline - No. 8)
The maximum value of the function $$f(x) = 2{x^3} - 15{x^2} + 36x - 48$$ on the set $$A = \{ x|{x^2} + 20 \le 9x|\} $$ is __________.
Answer
7
Explanation
We have,
$$f'(x) = 6(x - 2)(x - 3)$$
Hence, $$f(x)$$ is increasing in $$(3,\infty )$$.
Also, $$A = \{ 4 \le x \le 5\} $$
Therefore, $${f_{\max }} = f(5) = 7$$
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