Question
Download Solution PDFFind the value of x for which f(x) = x - ex is an increasing function
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) = x - ex
Differentiating with respect to x, we get
⇒ f’(x) = 1 - ex
For increasing function,
f'(x) > 0
⇒ 1 – ex > 0
⇒ ex < 1
⇒ ex < e0
∴ x < 0
So, x ∈ (-∞, 0)
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