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

NDA 2021 · Mathematics · Application of Derivatives

Consider the following statements in respect of the function...

Consider the following statements in respect of the function f(x)=x2+1f(x)=x^2+1 in the interval (1,2)(1,2). 1. The maximum value of the function is 5. 2. The minimum value of the function is 2. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

D. Neither 1 nor 2

Step-by-step solution

Hence, f(x)=x2+1f(x)=x^2+1f′(x)=2x when f′(x)=0⇒x=0 but x=0,∉(1,2)\begin{aligned} & f^{\prime}(x)=2 x \\ & \text{ when } f^{\prime}(x)=0 \Rightarrow x=0 \\ & \text{ but } x=0, \notin(1,2) \end{aligned}∴f(x)\therefore f(x) does not have any maxima and minima for the given interval.
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