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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives2 Marks
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 $f(x) = x^4- 62 x^2 + ax + 9$
$\Rightarrow f'\left( x \right) = 4{x^3} - 124x + a$
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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