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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 Revision for JEE

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Revise Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable by covering every subtopic once, drilling formulas, then solving 36+ timed MCQs with full solutions.

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Revision checklist

  1. 1.Core idea: Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
  2. 2.Relates to other subtopics in Limit, Continuity and Differentiability
  3. 3.Limits and continuity
  4. 4.Chain rule, implicit, logarithmic differentiation
  5. 5.Master Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable definitions and standard results
  6. 6.Solve 20 timed MCQs for Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable

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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