CONCEPT OF DERIVATIVES

MATHEMATICS

GRADE 11

DERIVATIVES

Chapter: 13.1

Smart Classroom

By Ghanashyam Adhikari

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📖 First Principles of Derivatives (प्रारम्भिक सिद्धान्त)

Select a function below to explore the step-by-step calculus proofs.

📈 Geometric Derivative Visualizer

Drag the slider below to reduce interval \(h\) to \(0\). Watch the green secant converge to the red tangent line.

Interval Controller

Interval distance (h): h = 3.60

Limit (h → 0) Max h

Secant Line Slope (Average Rate): 0.455

Tangent Line Slope (Instantaneous Derivative): 0.732

🌎 Real-Life Application of Calculus

Explore physical simulations demonstrating instantaneous rates of change.

Application 1: Physics

Falling Object (Kinematics Rate)

A ball falling under gravity follows: \(s(t) = 4.9t^2\). Differentiate to find velocity.

Position \(s(t)\): 0.0m

Instantaneous Velocity \(\frac{ds}{dt}\): 0.0m/s

Time elapsed (t seconds): 0.00s

Application 2: Optimization

Maximizing Box Volume

Cutting squares of size \(x\) from corners of a \(10\times10\) cardboard sheet: \(V(x) = x(10-2x)^2\).

Box V(x)

Cut-out \(x\): 1.00

Volume \(V(x)\): 64.0

Rate \(\frac{dV}{dx}\): 12.00

Cut height (x): 1.00

📝 Grade 11 Class Exam Quizzes (NEB Nepal)

Tap a question number below to review, work with your stylus on top, or expand step solutions.

10 Questions

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Calculus Board System v4.1 • GRADE 11