Question
Download Solution PDFFind the set of value of x for which f(x) = tan-1 x is increasing in
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- If f′(x) > 0 then the function is said to be increasing.
- If f′(x) < 0 then the function is said to be decreasing.
Calculation:
Given:
f(x) = tan-1 x
Differentiating with respect to x, we get
As we know that, x2 > 0 for x ∈ R
⇒ 1 + x2 > 0 for x ∈ R
So, 1 + x2 gives positive values for x ∈ R
Therefore, f’(x) > 0 for x ∈ R
Hence f(x) is increasing in x ∈ R or x ∈ (-∞,∞)
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