Question
If at x = 1 function $x^4-62 x^2+a x+9$ attains its maximum value, in the interval [0, 2], then find the value of a.
✓
Answer
$f(x)=x^4-62 x^2+a x+9$
Therefore, $f^{\prime}(x)=4 x^3-124 x+a$
f attains its maximum value on the interval [0, 2] at x = 1
Therefore, $f^{\prime}(1)=0$
4 - 124 + a = 0
a = 120
Therefore, $f^{\prime}(x)=4 x^3-124 x+a$
f attains its maximum value on the interval [0, 2] at x = 1
Therefore, $f^{\prime}(1)=0$
4 - 124 + a = 0
a = 120
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