Applications of Derivatives
A ladder slides down a wall, a balloon fills with air, a tank fills with water. In each case one quantity changes and drags another with it. The derivative tells you how fast. In this chapter you use it to follow such changes, to find where a graph rises and falls, to draw the tangent and the normal at a point, and to estimate small changes and errors. Then you find the largest and the smallest values of a quantity and use them to design the cheapest tin, the biggest box and the shortest fence. Python checks the numbers on every page. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level Pure Maths, IB Analysis and Approaches and AP Calculus.
Part of Mathematics · High School (11–12) (chapter 10)
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Rates of Change and Monotonic Functions
The derivative tells how fast one quantity changes when another changes. Use it to follow a moving particle and a changing cost. Solve related rates with a ladder, a balloon, a filling cone and a shadow. Then find where a function increases or decreases from the sign of its derivative. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
Tangents, Normals and Approximations
The derivative is the gradient (also called the slope) of a curve at a point. Write the equations of the tangent and the normal, find where a tangent is horizontal, parallel or perpendicular to a given line, and measure the angle between two curves. Then use differentials to estimate small changes, roots and percentage errors. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.