g(x) = x⁴f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6. A) 1,792 B) 1,024 C) 2,304 D) 4,608 E) 1,536

Name: g(x) = x 4 f(x). Find g'(4), given that f(4) = 3 and f '(4) = 6. A) 1,792 B) 1,024 C) 2,304 D) 4,608 E) 1,536
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Question

Quizplus · Accepted Answer

Using the product rule for differentiation, g'(x) = 4x^3f(x) + x^4f'(x). Substituting x = 4, f(4) = 3, and f'(4) = 6, we get g'(4) = 4(4^3)(3) + (4^4)(6) = 2,304.

G(x) = X4f(x)

G(x) = X⁴f(x)