Let f : R → R , f x = x 4 - 8 x 3 + 22 x 2 - 24 x + c . If sum of all local extremum values of f x is 1 , then c is equal to

Question

Let f : R → R , f x = x 4 - 8 x 3 + 22 x 2 - 24 x + c . If sum of all local extremum values of f x is 1 , then c is equal to, 8, 9, 10, 11

MARKS App · Accepted Answer

f ′ x = 4 x 3 − 6 x 2 + 11 x − 6 = 4 x - 1 x - 2 x - 3 Hence, x = 1 , 2 , 3 are points of extrema So, f 1 + f 2 + f 3 = 1 c - 9 + c - 8 + c - 9 = 1 ⇒ c = 9

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