The maximum value of $f (x) = x^{3} - 9 x^{2} + 24 x + 5$ in the interval $[1, 6]$

21

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25

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41

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46

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Solution

The correct option is C $41$
$f (x) = x^{3} - 9 x^{2} + 24 x + 5, x ϵ [1, 6]$
$f^{'} (x) = 3 x^{2} - 18 x + 24 = 0$
$x^{2} - 6 x + 8 = 0$
$x = 2, 4 ϵ (1, 6)$

x 1 2 4 6

f(x) 21 25 21 41

$∴$ Maximum value of $f (x) = 41$

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