Question

If the function f(x) = x⁴ - 62x² + ax + 9 attains a local maximum at x = 1, then a = _________________.

Answer 1

It is given that, the function f(x) = x⁴ − 62x² + ax + 9 attains a local maximum at x = 1.

$\therefore f\text{'}\left(x\right)=0$ at x = 1

f(x) = x⁴ − 62x² + ax + 9

Differentiating both sides with respect to x, we get

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

Now,

$f\text{'}\left(1\right)=0$

$\Rightarrow 4\times {\left(1\right)}^3-124\times 1+a=0$

$\Rightarrow a=124-4=120$

Thus, the value of a is 120.

Also,

$f\text{'}\text{'}\left(x\right)=12x^2-124$

At x = 1, we have

$f\text{'}\text{'}\left(1\right)=12\times {\left(1\right)}^2-124=12-124=-112<0$

So, x = 1 is the point of local maximum of f(x).


If the function f(x) = x⁴ − 62x² + ax + 9 attains a local maximum at x = 1, then a = ___120____.