Maths · Class 12 · Chapter 6
Application of Derivatives
12 lessons 96 min 3 simulations
The derivative measures how fast one quantity changes against another, and this chapter puts that to work. It turns rates into answers for growing circles, filling tanks and moving shadows, reads marginal cost and revenue in economics, uses the sign of f′ to tell where a function rises or falls, and locates the highest and lowest points of a graph with the first and second derivative tests. It ends with optimisation: setting up one quantity to be made largest or smallest, and checking every candidate on a closed interval.
What the exam asks
JEE Main asks for rates such as dA/dt or dh/dt at a given instant, the intervals on which a polynomial or trigonometric function is increasing or decreasing, the local maximum and minimum values of a cubic or quartic, the absolute extremes on a closed interval, and word problems on boxes, fences, cones and profit. Tangents and normals are outside the rationalised NCERT text but still appear in JEE Advanced; they are in the last section. Marks go on forgetting the end points of a closed interval, calling every critical point an extremum, trusting a zero second derivative, and using a rate before the relation between the variables has been set up.
Lessons
12 lessons · 96 min
1Rate of changeNCERT §6.1–6.210 min 1 sim2Related ratesNCERT §6.28 min3Marginal cost and revenueNCERT §6.26 min4Increasing and decreasing functionsNCERT §6.310 min 1 sim5Intervals from the sign of f′NCERT §6.37 min6Maxima and minimaNCERT §6.47 min7First derivative testNCERT §6.411 min 1 sim8Second derivative testNCERT §6.47 min9Optimisation problemsNCERT §6.4, Misc. Examples7 min10Absolute extrema on a closed intervalNCERT §6.4.16 min11Tangents and normalsNCERT §6.4, JEE extension6 min12Chapter reviewMust-know facts, traps and formulas11 min