The minimum value of f(x) = x^4 - x^2 - 2x + 6 is. - Vidyadip

MCQ

The minimum value of $f(x) = x^4 - x^2 - 2x + 6$ is.

A
$6$
✓
$4$
C
$8$
D
None of these.

✓

Answer

Correct option: B.

$4$

Given, $f(x) = x^4 - x^2 - 2x + 6$
$\Rightarrow f'(x) = 4x^3 - 2x - 2$
$\Rightarrow f'(x) = (x - 1)(4x^2 + 4x + 2)$
For a local maxima or a local minima, we must have $f'(x) = 0$
$\Rightarrow (x - 1)(4x^2 + 4x + 2) = 0$
$\Rightarrow (x - 1) = 0$
$\Rightarrow x = 1$
Now,$ f''(x) = 12x^2 - 2$
$\Rightarrow f''(x) = 12 - 2 = 10 > 0$
So, $x = 1$ is a local minima.
The local minimum value is given by
$f(1) = 1 - 1 -2 + 6 = 4$

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