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in Mathematics by (68.5k points)

यदि दिया है कि अन्तराल [0,2] में x = 1 पर फलन x4 – 62x2 + ax + 9 उच्चतम मान प्राप्त करता है तो a का मान ज्ञात कीजिए।

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माना f(x) = x4 – 62x2 + ax + 9

f‘(x) = 4x3 – 124x + a

उच्चतम व निम्नतम मान के लिए, f ‘(x) = 0

⇒ 4x3 – 124x + a = 0

दिया है, x = 1 पर, f उच्चतम है ⇒ f (1) = 0

4x3 – 124x + a = 0 में x = 1 रखने पर

4 x 1 – 124 x 1 + a = 0 ⇒ 4 – 124 + a = 0

⇒ – 120 + a = 0 a = 120

इसलिए a का मान 120 है।

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