The maximum value of function $x^{3} - 12 x^{2} + 36 x + 17$ in the interval [1, 10] is

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177

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None of these

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Solution

The correct option is B 177
Let $f (x) = x^{3} - 12 x^{2} + 36 x + 17$
$∴ f^{'} (x) = 3 x^{2} - 24 x + 36 = 0$ at x =2,6
Again f''(x)=6x-24 is -ve at x =2
So that f(6)=17, f(2)=49
At the end points f(1)=42, f(10)=177
So f(x) has its maximum value as 177.

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