Maths

Class 12

Maths · Class 12 · Chapter 5

Continuity and Differentiability

13 lessons 104 min 2 simulations

A function is continuous at a point when its graph arrives there without a break: the left-hand limit, the right-hand limit and the value all agree. It is differentiable there when the slopes of the chords on both sides settle on one finite number. This chapter tests continuity, shows that sums, products, quotients and composites of continuous functions stay continuous, proves that differentiable implies continuous, and builds the full toolkit of differentiation: the chain rule, implicit functions, inverse trigonometric functions, eˣ and log x, logarithmic differentiation, parametric forms and second derivatives.

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What the exam asks

JEE Main asks for the value of a constant (k, or a and b) that makes a piecewise function continuous, the points where [x] or |x|-type functions fail to be continuous or differentiable, and derivatives of composites, implicit relations, x-to-the-power-x forms, parametric curves and second derivatives that satisfy a given equation. Rolle's theorem and the mean value theorem are outside the rationalised NCERT text but remain standard JEE tools; they are in the last section. Marks go on forgetting the inner derivative in the chain rule, on treating y as a constant in implicit work, on using the power rule for xˣ, and on claiming that continuous means differentiable.

Lessons

13 lessons · 104 min