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The function f(x) = 1 - x - x3 is decreasing for1. x ≥ \(\frac {-1} 3\)2. x 14. All values of x |
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Answer» Correct Answer - Option 4 : All values of x Concept:
Calculation: Given: f(x) = 1 - x - x3 Differentiating with respect to x, we get ⇒ f'(x) = 0 - 1 - 3x2 ⇒ f'(x) = - 1 - 3x2 For decreasing function, f'(x) < 0 ⇒ -1 - 3x2 < 0 ⇒ -(1 + 3x2) < 0 As we know, Multiplying/Dividing each side of an inequality by a negative number reverses the direction of the inequality symbol. ⇒ (1 + 3x2) > 0 As we know, x2 ≥ 0, x ∈ R So, 1 + 3x2 > 0, x ∈ R Hence, the function is decreasing for all values of x |
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