f(x) = |x|: continuous at 0 but not differentiable theref(x) = |x|: 0 पर संतत पर अवकलनीय नहींf(x) = |x|: 0 par continuous par differentiable nahi

NCERT Section 5.3 · Class 12 Maths · Chapter 5 · interactive diagram

Parts and what they mean

• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
• Left arm y = -x (बायीं भुजा y = -x) — Slope -1: left hand derivative at 0 is \frac{-h}{h} = -1.
• Right arm y = x (दायीं भुजा y = x) — Slope +1: right hand derivative at 0 is \frac{h}{h} = 1.
• Corner at (0, 0) ((0, 0) पर कोना) — Continuous (no break), but -1 \ne 1, so f'(0) does not exist.

Original diagram drawn by Simple Learning Hub, based on NCERT Section 5.3. Report a mistake