Question
Download Solution PDFIf the function f(x) = x2 - kx is monotonically increasing in the interval (1, ∞), then which one of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
Differentiation Formula:
Calculation:
f(x) = x2 - kx
⇒ f'(x) = 2x - k
Since, f is monotonic increasing.
f'(x) > 0
⇒ 2x - k > 0
⇒ k < 2x ----(1)
Since, we have 1 < x < ∞
⇒ 2 < 2x < ∞ ----(2)
From (1) and (2), we get
k < 2
∴ The correct relation is k < 2.
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