Calculus with Spreadsheets: Rates of Change, Optimisation & Area

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Drop a package from a delivery drone, compute its average speed over shorter and shorter intervals and see the numbers settle on the instantaneous speed, the derivative.
• Tabulate a cubic, estimate its derivative from the table with central differences, compute the exact slope at x₀ and draw the function together with its tangent line.
• Model Kestrel Bikes' monthly cost and revenue, estimate marginal cost from a table, compute it exactly with the derivative and decide whether one more bike adds profit.
• Tabulate Kestrel's profit around the peak, watch the derivative change sign, pick the best output on the grid and solve P′(q) = 0 for the exact optimum.
• Model Kestrel's helmet demand with an exponential curve, estimate dQ/dp numerically, turn it into the point elasticity and find the price where revenue peaks.
• Turn a Kestrel e-bike's speed curve into distance travelled with the trapezoid rule and Simpson's rule, then compare both with the exact integral.
• Find the equilibrium of a market with a curved demand line, measure the area between the demand curve and the price line numerically and exactly, and compare it with the producer surplus.
• Grow Kestrel's cash reserve with continuous compounding, chart it against annual compounding, read off the instantaneous growth rate with a derivative and turn a decay constant into a half-life.