Question
Download Solution PDFThe function f(x) = 1 + x2 + x4 is strictly increasing 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 + x2 + x4
Differentiating with respect to x, we get
⇒ f'(x) = 0 + 2x + 4x3
⇒ f'(x) = 2x + 4x3
For strictly increasing function, f'(x) > 0
⇒ 2x + 4x3 > 0
⇒ 2x(1 + 2x2) > 0
As we know, x2 ≥ 0, x ∈ R
So, 1 + 2x2 > 0, x ∈ R
Now, 2x > 0
⇒ x > 0
Hence function is strictly increasing for x > 0
Last updated on Jul 4, 2025
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