If f x = c o s - 1 x 3 2 - 1 - x - x 2 + x 3 , ∀ 0 ≤ x ≤ 1 , then the minimum value of f x is

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Question: Answered & Verified by Expert

If

f (x) = c o s^{- 1} (x^{\frac{3}{2}} - \sqrt{1 - x - x^{2} + x^{3}}), \forall 0 \leq x \leq 1

, then the minimum value of

f (x)

is

MathematicsInverse Trigonometric FunctionsJEE Main

Solution:

1623 Upvotes Verified Answer

The correct answer is: 0

$f (x) = c o s^{- 1} \{x \sqrt{x} - \sqrt{(1 - x) (1 - x^{2})}\}$
$= c o s^{- 1} \{x \sqrt{x} - \sqrt{1 - {(\sqrt{x})}^{2}} \sqrt{1 - x^{2}}\}$
$= c o s^{- 1} x + c o s^{- 1} \sqrt{x}$

At $x = 1$ ,

minimum value of $f (x) = 0$

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