Local maximum, local minimum and point of inflectionस्थानीय उच्चतम, स्थानीय निम्नतम और नति परिवर्तन बिंदुLocal maximum, local minimum aur point of inflection

NCERT Misc. Exercise Q10 · Class 12 Maths · Chapter 6 · interactive diagram

Parts and what they mean

• f(x) = (x - 2)^4 (x + 1)^3 (f(x) = (x - 2)^4 (x + 1)^3) — f'(x) = (x - 2)^3 (x + 1)^2 (7x - 2), zero at x = -1, \frac{2}{7}, 2.
• Local maximum at x = \frac{2}{7} (x = \frac{2}{7} पर स्थानीय उच्चतम) — A hill top: f' goes from + to -; the tangent is horizontal.
• Local minimum at x = 2 (x = 2 पर स्थानीय निम्नतम) — A valley bottom: f' goes from - to +; local minimum value f(2) = 0.
• Point of inflection at x = -1 (x = -1 पर नति परिवर्तन बिंदु) — f'(-1) = 0 but f' stays + on both sides (the factor (x + 1)^2), so it is neither max nor min.
• 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 Misc. Exercise Q10. Report a mistake