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Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable Concepts for JEE

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Master Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable is a core JEE Main Mathematics subtopic under Limit, Continuity and Differentiability. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

  • Understand the definition and scope of Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable in the JEE syllabus
  • Memorise key formulas and standard results linked to Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

  • Revise Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable and reattempt after 48 hours

Common trap

Students often rush Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 7: Limit, Continuity and Differentiability
If the radius of a sphere is measured as 9cm9 \mathrm{cm} with an error of 0.03cm0.03 \mathrm{cm} then, find the approximate error in calculating its volume
Q2MathsUnit 7: Limit, Continuity and Differentiability
If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is λ%,\lambda \%, then the error in its volume is
Q3MathsUnit 7: Limit, Continuity and Differentiability
Function f(x)=(x+2)e−x\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}} is
Q4MathsUnit 7: Limit, Continuity and Differentiability
The two curves x3−3xy2+2=0x^{3}-3 x y^{2}+2=0 and 3x2y−y3−2=0\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0}
Q5MathsUnit 7: Limit, Continuity and Differentiability
Equation of normal drawn to the graph of the function defined as f(x)=sin⁡x2xf(x)=\frac{\sin x^{2}}{x} x≠0\boldsymbol{x} \neq \mathbf{0} and f(0)=0\boldsymbol{f}(\mathbf{0})=\mathbf{0} at the origin is?
Q6MathsUnit 7: Limit, Continuity and Differentiability
The point on the curve y=x2y=x^{2} which is nearest to (3,0) is
Q7MathsUnit 7: Limit, Continuity and Differentiability
For x∈R\boldsymbol{x} \in \boldsymbol{R} let f(x)=∣sin⁡x∣\boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}| and g(x)=∫0xf(t)dt.g(x)=\int_{0}^{x} f(t) d t . Let p(x)=g(x)−2πxp(x)=g(x)-\frac{2}{\pi} x Then
Q8MathsUnit 7: Limit, Continuity and Differentiability
The normals to the curve y=x2−x+y=x^{2}-x+ 1, drawn at the points with the abscissa x1=0,x2=−1\boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1} and x3=52\boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}}

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Focus on core ideas across Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable. JEE tests application, not just memorisation.

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