Let f x be continuous on 0 , 6 and differentiable on 0 , 6 Let f 0 = 12 and f 6 = - 4 . If g x = f x x + 1 , then for some Lagrange's constant c ∈ 0 , 6 , g ' c =

Question

Let f x be continuous on 0 , 6 and differentiable on 0 , 6 Let f 0 = 12 and f 6 = - 4 . If g x = f x x + 1 , then for some Lagrange's constant c ∈ 0 , 6 , g ' c =, - 44 3, - 22 21, 32 21, 44 21

MARKS App · Accepted Answer

g x = f x x + 1 · f 0 = 12 , f 6 = - 4 C ∈ 0 , 6 ⇒ g 0 = f 0 0 + 1 = 12 1 = 12 ⇒ g 6 = f 6 6 + 1 = - 4 7 From Lagrange's theorem, g ' c = g 6 - g 0 6 - 0 = - 4 7 - 12 6 = - 88 42 ∴ g ' c = - 44 21

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