Increasing and decreasing: colour by the sign of f′वर्धमान और ह्रासमान: f′ के चिह्न से रंगIncreasing aur decreasing: f′ ke sign se rang

NCERT Example 17 · Class 12 Maths · Chapter 6 · interactive diagram

Parts and what they mean

• Increasing part (f'(x) > 0) (वर्धमान भाग (f'(x) > 0)) — For x < -1 and x > 1: f'(x) = 3(x-1)(x+1) > 0, the graph rises from left to right.
• Decreasing part (f'(x) < 0) (ह्रासमान भाग (f'(x) < 0)) — For -1 < x < 1: f'(x) < 0, the graph falls from left to right.
• Tangent going up (ऊपर जाती स्पर्श रेखा) — Where f increases, the tangent has positive slope f'(x).
• Tangent going down (नीचे जाती स्पर्श रेखा) — At x = 0 the slope is f'(0) = -3 < 0.
• Local maximum (-1, 5) (स्थानीय उच्चतम (-1, 5)) — f' changes from + to - at x = -1; local maximum value f(-1) = 5.
• Local minimum (1, 1) (स्थानीय निम्नतम (1, 1)) — f' changes from - to + at x = 1; local minimum value f(1) = 1.
• Sign of f'(x) (f'(x) का चिह्न) — + on (-\infty, -1), - on (-1, 1), + on (1, \infty).
• 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 Example 17. Report a mistake