The absolute minimum value of $x^4-x^2-2

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

The absolute minimum value of $x^4-x^2-2 x+5$

Options:

is equal to 5

is equal to 3

is equal to 7

does not exist

Correct Answer:

is equal to 3

Explanation:

$f(x)=x^4-x^2-2 x+5$

$f'(x) =4 x^3-2 x-2$

$=(x-1)\left(4 x^2+4 x+2\right)$

Clearly at x = 1, we will set the minimum value which is 3.