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The maximum value of the function f(x)=2...

The maximum value of the function `f(x)=2x^3-15 x^2+36 x-48` on the set `A={x|x^2|20lt=9x}` is______.

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The correct Answer is:
7
Given, ` A = { x |x^(2) + 20 le 9x } = {x | x in [4, 5]}`
` (##41Y_SP_MATH_C10_E04_069_S01.png" width="80%">
Now, ` f ' (x)= 6(x ^(2) - 5x + 6 )`
Put ` f ' (x) = 0 rArr x = 2, 3 `
` " " f (2) = - 20 , f(3) = - 21, f( 4) = - 16 , f ( 5) = 7`
From graph, maximum value of ` f (x)` on set A is ` f ( 5) = 7`.
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