Question
Download Solution PDFThe function f(x) = 1 - x - x3 is decreasing for
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- If f′(x) > 0 then the function is said to be strictly increasing.
- If f′(x) < 0 then the function is said to be decreasing.
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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