Homework SourseIf gx 2 3x x125 x x14 what is g 16SolutionBy product ru
If g(x) = (2 + 3x + x1/2)(5 - x + x1/4), what is g \'(16)?
Solution
By product rule,
g\'(x) = [3 + (1/2)x^(-1/2)][-1 + (1/4)x^(-3/4)]
Thus,
g\'(16) = [3 + (1/2)(16)^(-1/2)][-1 + (1/4)(16)^(-3/4)]
As 16^(-1/2) = 1/4, 16^(-3/4) = 1/8,
g\'(16) = [3 + (1/2)(1/4)][-1 + (1/4)(1/8)]
g\'(16) = [3 + 1/8][-1 + 1/32]
g\'(16) = -775/256 [ANSWER]
![If g(x) = (2 + 3x + x1/2)(5 - x + x1/4), what is g \'(16)?SolutionBy product rule, g\'(x) = [3 + (1/2)x^(-1/2)][-1 + (1/4)x^(-3/4)] Thus, g\'(16) = [3 + (1/2)(1](/WebImages/27/if-gx-2-3x-x125-x-x14-what-is-g-16solutionby-product-ru-1071031-1761561021-0.webp "If g(x) = (2 + 3x + x1/2)(5 - x + x1/4), what is g \'(16)?SolutionBy product rule, g\'(x) = [3 + (1/2)x^(-1/2)][-1 + (1/4)x^(-3/4)] Thus, g\'(16) = [3 + (1/2)(1")
