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Ex 6.5, 11 - At x = 1, function x4 - 62x2 + ax + 9 attains max - Absolute minima/maxima

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.5,11 It is given that at đ‘„ = 1, the function đ‘„4 – 62đ‘„2 + đ‘Žđ‘„+ 9 attains its maximum value, on the interval [0, 2]. Find the value of a. We have fï·đ‘„ï·Ż=đ‘„4 – 62đ‘„2 + đ‘Žđ‘„+ 9 Finding fâ€™ï·đ‘„ï·Ż fâ€™ï·đ‘„ï·Ż=ï·đ‘‘ï·ï·đ‘„ï·ź4ï·Żâˆ’ 62ï·đ‘„ï·ź2ï·Ż + đ‘Žđ‘„ + 9ï·Żï·źđ‘‘đ‘„ï·Ż = ﷐4đ‘„ï·ź3ï·Żâˆ’62 ×2đ‘„+𝑎 = ﷐4đ‘„ï·ź3ï·Żâˆ’124đ‘„+𝑎 Given that at đ‘„=1, fï·đ‘„ï·Ż=ï·đ‘„ï·ź4ï·Żâˆ’62ï·đ‘„ï·ź2ï·Ż+đ‘Žđ‘„+9 attain its Maximum Value i.e. fï·đ‘„ï·Ż maximum at đ‘„=1 ∎ đ‘“â€™ï·đ‘„ï·Ż=0 at đ‘„=1 Now, f’﷐1ï·Ż=0 4﷐﷐1ï·Żï·ź3ï·Żâˆ’124﷐1ï·Ż+𝑎=0 4 – 124 + a = 0 – 120 + a = 0 a = 120 Hence a = 120

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