## Consider the following functions.G(x) = 4×2; f(x) = 8x(a) a. Verify that G is an antiderivative of f.G(x) is an antiderivative of f(x

Question

Consider the following functions.G(x) = 4×2; f(x) = 8x(a)

a. Verify that G is an antiderivative of f.G(x) is an antiderivative of f(x) because f ‘(x) = G(x) for all x.

A. G(x) is an antiderivative of f(x) because G(x) = f(x) for all x.

B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.

C. G(x) is an antiderivative of f(x) because G(x) = f(x) + C for all x.

D. G(x) is an antiderivative of f(x) because f(x) = G(x) + C for all x.

b. Find all antiderivatives of f. (Use C for the constant of integration.)

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2021-10-10T19:01:25+00:00
2021-10-10T19:01:25+00:00 1 Answer
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## Answers ( )

Answer:(a) B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.(b)Every function of the form is an antiderivative of 8xStep-by-step explanation:A function

Fis anantiderivativeof the functionfiffor all x in the domain of

f.(a)If , then is an antiderivative offbecauseTherefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.

Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of

f.(b)Becausethen is an antiderivative of . Therefore, every antiderivative of 8x is of the form for some constant C, and every function of the form is an antiderivative of 8x.