Episode 9 — Differential Calculus

Optimisation

Learners will be able to:

• Calculate the derivative of a cubic function in the form P(X) = -2X^3 + 600X + 1000. • Set the derivative equal to zero and solve for X to find the maximum profit. • Identify the relationship between the number of employees (X) and the maximum profit. • Differentiate the equation V = 6X^2 * H to find the derivative V' in terms of X. • Solve for X by setting the derivative V' equal to zero and finding the square root of both sides. • Substitute the value of X into the formula for H to determine the height of the box that maximizes the volume.