Derivative = slope of the tangent: the secant turns into the tangent as h → 0अवकलज = स्पर्श रेखा की ढाल: h → 0 पर छेदक रेखा स्पर्श रेखा बन जाती हैDerivative = slope of the tangent: the secant turns into the tangent as h → 0

Section 12.5 · Class 11 Maths Ch 12 · interactive diagram

Parts and what they mean

• Curve y = f(x) (वक्र y = f(x)) — Here f(x) = x²/2.
• Point A(a, f(a)) (बिंदु A(a, f(a))) — The point where we want the rate of change (here a = 1.5).
• Nearby point B (पास का बिंदु B) — x moves from a to a + h; f changes by f(a + h) − f(a).
• Small step h (छोटा कदम h) — Let h shrink to 0 — B slides towards A.
• Secant AB (छेदक रेखा AB) — Slope = [f(a + h) − f(a)]/h (average rate).
• Tangent at A (A पर स्पर्श रेखा) — Limit of the secants: its slope is f′(a). For x²/2, f′(a) = a = 1.5.
• Definition of derivative (अवकलज की परिभाषा) — f′(a) = lim(h→0) [f(a + h) − f(a)]/h, if the limit exists (first principle).

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 12. Report a mistake