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Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan 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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