Lesson Plan

• Describe the fundamental differentiation rules and apply them to compute derivatives of algebraic and transcendental functions.
• Determine and classify stationary points of a function using the first and second derivative tests.
• Derive equations of tangent and normal lines at a given point on a curve.
• Solve related‑rates problems by translating a word problem into a differentiated equation and interpreting the result.

• Projector and screen
• Whiteboard and markers
• Worksheet with differentiation practice problems
• Graphing calculators (or GeoGebra on laptops)
• Printed handout of differentiation rules and common function derivatives

Begin with the question, “How quickly does a car’s speed change at an exact instant?” to hook interest. Review that students already know basic function notation and simple algebraic manipulation. State that by the end of the lesson they will be able to differentiate functions, locate and classify stationary points, and set up related‑rates equations.

1. Do‑now (5'): Quick mental recall of the power rule; students write examples on the board.
2. Direct instruction (10'): Review all basic differentiation rules with projector slides and brief examples.
3. Guided practice (15'): Pairs complete worksheet differentiating a range of functions; teacher circulates to check understanding.
4. Stationary points activity (10'): Compute f′(x)=0 for a cubic, find candidate points, and classify them using the second‑derivative test.
5. Tangent & normal demonstration (10'): Derive the tangent and normal equations for y=x³‑3x²+2 at x=1; students sketch the curve and lines.
6. Related‑rates mini‑investigation (15'): Solve the expanding‑circle and ladder‑sliding problems in small groups, then share solutions.
7. Summary & check for understanding (5'): Quick exit quiz via clickers covering key concepts.

Recap the four main ideas: differentiation rules, stationary point classification, tangent/normal equations, and the related‑rates procedure. For the exit ticket, ask each student to write one real‑world situation where differentiation is useful. Assign homework: complete the remaining worksheet problems on stationary points and related‑rates.