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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2018 · Mathematics · Application of Derivatives

In which one of the following intervals is the function f(x)=x^2-5...

In which one of the following intervals is the function f(x)=x2−5x+6f(x)=x^2-5 x+6 decreasing?

Options

  1. A(−∞,2](-\infty, 2]
  2. B[3,∞][3, \infty]
  3. C(−∞,∞)(-\infty, \infty)
  4. D(2,3)(2,3)

Correct answer

A. (−∞,2](-\infty, 2]

Step-by-step solution

f(x)=x2−5x+6⇒f′(x)=2x−5⇒f′(x)<0⇒2x−5<0⇒x<52\begin{aligned} & f(x)=x^2-5 x+6 \\ & \Rightarrow f^{\prime}(x)=2 x-5 \\ & \Rightarrow f^{\prime}(x) < 0 \\ & \Rightarrow 2 x-5 < 0 \Rightarrow x < \frac{5}{2}\end{aligned}
Hence, f(x)f(x) is decreasing in (−∞,2.5](-\infty, 2.5]
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