Secant → tangent: the derivative is a limit of slopesछेदक रेखा → स्पर्श रेखा: अवकलज ढालों की सीमा हैSecant → tangent: derivative slopes ki limit hai

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.
• Curve y = x^2 (वक्र y = x^2) — The function we differentiate at c = 1.
• Point P(1, 1) (बिंदु P(1, 1)) — The point where we want the slope: c = 1.
• Point Q(2, 4) (बिंदु Q(2, 4)) — A second point at c + h with h = 1. Slide it towards P to make h \to 0.
• Secant PQ, slope 3 (छेदक रेखा PQ, ढाल 3) — Slope = \frac{f(c + h) - f(c)}{h} = \frac{4 - 1}{1} = 3; in general 2 + h for this curve.
• Tangent at P, slope 2 (P पर स्पर्श रेखा, ढाल 2) — As h \to 0, slope 2 + h \to 2 = f'(1).
• Run h = 1 (क्षैतिज दूरी h = 1) — Change in x between P and Q.
• Rise f(c + h) - f(c) = 3 (ऊर्ध्वाधर परिवर्तन f(c + h) - f(c) = 3) — Change in y: 4 - 1 = 3.

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