It is given that at x = 1, the function x4 - 62x2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.

Question

It is given that at x = 1, the function x4 - 62x2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a. (A) 100 (B) 120 (C) 140 (D) 160

Tardigrade Admin · Accepted Answer

Let f(x) = x4 - 62x2 + ax + 9. Then, f(x) = 4x3 - 124x + a. It is given that f(x) attains its maximum at x = 1. ∴ f'( 1 ) = 0 ⇒ 4 - 124 + a = 0 ⇒ a = 120

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

$100$

$120$

$140$

$160$

Let $f (x) = x^{4} - 62 x^{2} + a x + 9$ . Then,
$f (x) = 4 x^{3} - 124 x + a$ .
It is given that $f (x)$ attains its maximum at $x = 1$ .
$∴ f^{'} (1) = 0$
$\Rightarrow 4 - 124 + a = 0$
$\Rightarrow a = 120$

Q. It is given that at x=1, the function x4−62x2+ax+9 attains its maximum value on the interval [0,2]. Find the value of a.

100

120

140

160