Family of anti derivatives of 2x: y = x² + C2x के प्रतिअवकलजों का कुल: y = x² + C2x ke anti derivatives ki family: y = x² + C

NCERT Explainer (7.2) · Class 12 Maths · Chapter 7 · interactive diagram

Parts and what they mean

• Tangents at x = 1 — all parallel (x = 1 पर स्पर्श रेखाएँ — सभी समांतर) — At x = 1 every curve has slope \dfrac{d}{dx}(x^2 + C) = 2x = 2. Same derivative, so the tangents are parallel.
• Points (1, 1 + C) (बिंदु (1, 1 + C)) — Where the line x = 1 meets each member of the family.
• The line x = 1 (रेखा x = 1) — Move along this line: the curves differ only by a vertical shift C.
• y = x^2 - 2 (y = x^2 - 2) — One anti derivative of 2x (C = -2). Its derivative is 2x.
• y = x^2 - 1 (y = x^2 - 1) — One anti derivative of 2x (C = -1). Its derivative is 2x.
• $y = x^2 $ ($y = x^2 $) — One anti derivative of 2x (C = 0). Its derivative is 2x.
• y = x^2 + 1 (y = x^2 + 1) — One anti derivative of 2x (C = 1). Its derivative is 2x.
• y = x^2 + 2 (y = x^2 + 2) — One anti derivative of 2x (C = 2). Its derivative is 2x.
• 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.

Original diagram drawn by Simple Learning Hub, based on NCERT Explainer (7.2). Report a mistake