Let x 0 be the point of local maxima of f x = a → · b → × c → , where a → = x i ^ - 2 j ^ + 3 k ^ , b → = - 2 i ^ + x j ^ - k ^ and c → = 7 i ^ - 2 j ^ + x k ^ . Then the value of a → · b → + b → · c → + c → · a → at x = x 0 is:

Question

Let x 0 be the point of local maxima of f x = a → · b → × c → , where a → = x i ^ - 2 j ^ + 3 k ^ , b → = - 2 i ^ + x j ^ - k ^ and c → = 7 i ^ - 2 j ^ + x k ^ . Then the value of a → · b → + b → · c → + c → · a → at x = x 0 is:, - 4, - 30, 14, - 22

MARKS App · Accepted Answer

f x = a → b → c → = x − 2 3 − 2 x − 1 7 − 2 x = x x 2 − 2 + 2 − 2 x + 7 + 3 4 − 7 x = x 3 − 2 x − 4 x + 14 + 12 − 21 x f x = x 3 − 27 x + 26 f ' x = 3 x 2 − 27 = 3 x − 3 x + 3 so local maxima point is x 0 = - 3 Now a → . b → + b → . c → + c → . a → = − 2 x − 2 x − 3 - 14 − 2 x − x + 7 x + 4 + 3 x = 3 x − 13 at x = x 0 = − 3 a → . b → + b → . c → + c → . a → = − 9 − 13 = − 22

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