Continuity and Differentiability Case Study Questions Class 12 Maths Chapter 5

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Last Updated on July 21, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class Class 12 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class Class 12 Maths. In this article, you will find case study questions for cbse class Class 12 Maths chapter 5 Continuity and Differentiability.

Chapter	Continuity and Differentiability
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	Class 12
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 12 Maths Chapterwise Case Study

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Table of Contents

Case Study Questions on Continuity and Differentiability

Case Study Question 1

Case Study:
A pharmaceutical company is modeling the amount of drug (D, in mg) present in a patient’s bloodstream over time (t, in hours) by the following function:

\[ f(t) = \begin{cases} t^2 + 2t, & \text{for } 0 \leq t \leq 2 \\ 4t + k, & \text{for } 2 < t \leq 5 \end{cases} \]

Here, k is a constant to be determined. The company requires the drug level in the bloodstream to increase smoothly at t=2 hours, the time when the mode of drug administration changes.

What value of k will make the function f(t) continuous at t = 2 hours?
For the value of k obtained above, is the function f(t) differentiable at t = 2 hours?
Explain in the drug administration context what continuity and differentiability signify.

Solutions:

1. Value of k for Continuity at t = 2:

Let \( f(t) \) be continuous at \( t = 2 \): \[ \lim_{t \to 2^-} f(t) = \lim_{t \to 2^+} f(t) = f(2) \] From the left (\( t \leq 2 \)): \[ \lim_{t \to 2^-} f(t) = 2^2 + 2 \times 2 = 4 + 4 = 8 \] From the right (\( t > 2 \)): \[ \lim_{t \to 2^+} f(t) = 4 \times 2 + k = 8 + k \] Set equal for continuity: \[ 8 = 8 + k \implies k = 0 \]

2. Differentiability at t = 2:

Find the left and right derivatives at \( t = 2 \): For \( t \leq 2 \), \( f(t) = t^2 + 2t \): \[ f’_-(2) = \frac{d}{dt} (t^2 + 2t) = 2t + 2 \Rightarrow f’_-(2) = 2 \times 2 + 2 = 6 \] For \( t > 2 \), \( f(t) = 4t + 0 = 4t \): \[ f’_+(2) = \frac{d}{dt} (4t) = 4 \Rightarrow f’_+(2) = 4 \] Since \( f’_-(2) \neq f’_+(2) \), \( f(t) \) is not differentiable at \( t = 2 \).

3. Real-life interpretation:

Continuity at \( t = 2 \) means the concentration of the drug in the bloodstream does not suddenly jump or drop at the time the method of administration changes.
Differentiability means the rate of change of drug concentration (how fast it is increasing) is the same from both sides at \( t = 2 \). In this case, it’s not differentiable; the rate changes abruptly, but the amount itself does not jump.

We hope the given case study questions for Continuity and Differentiability Class Class 12 helps you in your learning.

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Topics from which case study questions may be asked

Continuity (Algebraic, Trigonometric, Exponential, Logarithmic)
Differentiability
Derivatives of Composite Functions, Inverse Trig Functions, Implicit Functions
Exponential and Logarithmic Differentiation
Logarithmic Differentiation Technique
Second Order Derivatives
Mean Value Theorems (Rolle’s and Lagrange’s)

Continuity ensures a function has no breaks, while differentiability allows computation of rate of change, forming the base of calculus.

Frequently Asked Questions (FAQs) on Continuity and Differentiability Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 12 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing Continuity and Differentiability case study questions?

A12: We provide case study questions for CBSE Class 12 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.