It is given that at x = 1, the function x^4 - 62 x^2 + ax + 9 att… - Vidyadip

Question

It is given that at x = 1, the function ${x^4} - 62{x^2} + ax + 9$ attains its maximum value, on the interval [0, 2]. Find the value of a.

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Answer

Let f(x) = x⁴- 62 x² + ax + 9

$\Rightarrow f'\left( x \right) = 4{x^3} - 124x + a$

Since, f(x) attains its maximum value at x = 1 in the interval [0, 2], therefore $f'\left( 1 \right) = 0$

$\therefore f'\left( 1 \right) = 4 - 124 + a = 0$

$\Rightarrow a - 120 = 0$

$\Rightarrow a = 120$

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