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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

If the function f(x)=x^2-k x is monotonically increasing in the...

If the function f(x)=x2−kxf(x)=x^2-k x is monotonically increasing in the interval (1,∞)(1, \infty), then which one of the following is correct?

Options

  1. Ak<2k < 2
  2. B2<k<32 < k < 3
  3. C3<k<43 < k < 4
  4. Dk>4k > 4

Correct answer

A. k<2k < 2

Step-by-step solution

f(x)=x2−kxf′(x)=2x−k\begin{aligned} & f(x)=x^2-k x \\ & f^{\prime}(x)=2 x-k \end{aligned} For monotonically increasing in (1,∞)(1, \infty)f′(x)>0⇒2x−k>0⇒k<2x,x∈(1,∞)\begin{aligned} & f^{\prime}(x) > 0 \\ & \Rightarrow 2 x-k > 0 \\ & \Rightarrow k < 2 x, x \in(1, \infty) \end{aligned}ork<2or k < 2
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