Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2024 · Mathematics · Application of Derivatives

A differentiable function f(x) has a local maximum at x=0 . Let y=2...

A differentiable function f(x)f(x) has a local maximum at x=0x=0. Let y=2f(x)+ax−by=2 f(x)+a x-b. Which of the following is/are correct? 1. f′(0)=02.f^{\prime}(0)=0 2.f^{\prime \prime}(0) < 0Selectthecorrectanswerusingthecodegivenbelow:Select the correct answer using the code given below:

Options

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

Correct answer

C. Both 1 and 2

Step-by-step solution

Given, y=2f(x)+ax−b....(i)\quad y=2 f(x)+a x-b\qquad....(i) Differentiating both side w.r. to xx⇒dydx=2f′(x)+a(1)....(ii)d2ydx2=2f′′(x)....(iii)\begin{aligned} \Rightarrow \quad \frac{d y}{d x} & =2 f^{\prime}(x)+a(1) \qquad....(ii) \\ \frac{d^2 y}{d x^2} & =2 f^{\prime \prime}(x) \qquad....(iii) \end{aligned}∵f(x)\because f(x) has a local maximum at x=0x=0 Hence, f′(0)=0f^{\prime}(0)=0 and f′′(0)<0....(iv)f^{\prime \prime}(0) < 0\qquad....(iv) Therefore option (C) is correct.
Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is… NDA 2026Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . What is… NDA 2025Consider the following statements regarding the function f(x) = (1)/(x - 5)… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025A wire of length 20 cm is to be bent into a rectangle. Which of the following statements… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = x^2 +… NDA 2025For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . The… NDA 2025Consider the following for the two (02) items that follow: The slope of the tangent to… NDA 2025For the following three (03) items: Consider the function f(x) = x|x| . Consider the… NDA 2025Consider the following statements: Statement-I: The function f(x) = (x^3 + 128)/(x) has a… NDA 2025Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the greatest value of… NDA 2024Let f(x)=(x)/( x) ;(x > 1) Consider the following statements: 1. f(x) is increasing in… NDA 2024Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the least value of… NDA 2024 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs