Ch 4Applications of Derivatives — Class 12 Mathematics and Statistics, concept-first.

Once we can differentiate a function, the derivative becomes a powerful tool for describing how the function behaves — whether its values are rising or falling, where it turns, and where it reaches a…

A point where a function stops rising and begins to fall (or stops falling and begins to rise) is of special interest: it is where the function attains a local maximum or a local minimum.

The first derivative test works in every case, but it requires checking the sign of on both sides of each critical point.

The most direct commercial use of the derivative is marginal analysis — measuring the effect on cost, revenue or profit of producing or selling one more unit.

Demand for a good depends on its price: usually, the higher the price , the smaller the quantity demanded .

The techniques of maxima and minima (Sections 2–3) combine with the cost–revenue functions (Section 4) to answer the questions a business most wants answered: what output maximises profit? and what ou…

Sample papers and previous-year board questions for this subject.