Absolute maximum and minimum on a closed intervalसंवृत अंतराल पर निरपेक्ष उच्चतम और निम्नतमClosed interval par absolute maximum aur minimum

NCERT Example 27 · Class 12 Maths · Chapter 6 · interactive diagram

Parts and what they mean

• f(x) = 2x^3 - 15x^2 + 36x + 1 on [1, 5] ([1, 5] पर f(x) = 2x^3 - 15x^2 + 36x + 1) — f'(x) = 6(x - 2)(x - 3): critical points x = 2, 3.
• End points x = 1 and x = 5 (अंत्य बिंदु x = 1 और x = 5) — Always include them (Working Rule, Step 2).
• Absolute maximum value 56 (निरपेक्ष उच्चतम मान 56) — f(5) = 56 is the largest of 24, 29, 28, 56 — it occurs at an end point.
• Absolute minimum value 24 (निरपेक्ष निम्नतम मान 24) — f(1) = 24 is the smallest — also at an end point.
• Local maximum f(2) = 29 (स्थानीय उच्चतम f(2) = 29) — A local hill, but not the absolute maximum (56 is bigger).
• Local minimum f(3) = 28 (स्थानीय निम्नतम f(3) = 28) — A local valley, but not the absolute minimum (24 is smaller).
• 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 27. Report a mistake