Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

A function is defined in (0, ∞) by f(x)=\ array ccc 1-x^2 & for & 0...

A function is defined in (0,∞)(0, \infty) by f(x)=\left\{1−x2 for 0<x≤1 In x for 1<x≤2ln⁡2−1+0.5x for 2<x<∞\begin{array}{ccc}1-x^2 & \text{ for } & 0 < x \leq 1 \text{ In } & x & \text{ for } 1 < x \leq 2 \ln 2-1+0.5 x & \text{ for } & 2 < x < \infty\end{array}\right. Which one of the following is correct in respect of the derivative of the function, i.e., f′(x)f^{\prime}(\mathrm{x}) ?

Options

  1. Af′(x)=2xf^{\prime}(x)=2 x for 0<x≤10 < x \leq 1
  2. Bf′(x)=−2xf^{\prime}(\mathrm{x})=-2 \mathrm{x} for 0<x≤10 < \mathrm{x} \leq 1
  3. Cf′(x)=−2xf^{\prime}(x)=-2 x for 0<x<10 < x < 1
  4. Df′(x)=0f^{\prime}(\mathrm{x})=0 for 0<x<∞0 < x < \infty

Correct answer

C. f′(x)=−2xf^{\prime}(x)=-2 x for 0<x<10 < x < 1

Step-by-step solution

f(x)=\left\{1−x2 for 0<x≤1ln⁡x for 1<x≤2ln⁡2−1+0.5x for 2<x<∞\begin{array}{l}1-x^2 \text{ for } 0 < x \leq 1 \\ \ln x \text{ for } 1 < x \leq 2 \\ \ln 2-1+0.5 x \text{ for } 2 < x < \infty\end{array}\right.f^{\prime}(x)=-2 x for 0<x<10 < x < 1
Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

What is the derivative of (x)/(|x|) with respect to x , where x< 0 ? NDA 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f ^ ∘ g(x) , then which… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of… NDA 2026If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is… NDA 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025Paragraph: Let f(x)=[x]^2- [x^2] . Question: Consider the following statements: A. f(x)… NDA 2024Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array . If the function f(x) is… NDA 2023 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs