Question

Find f(x) if f'(x) = 7 / x^4 and f(1) = 4.

A. f(x) = -7 / 3 x^-3 - 3
B. f(x) = -28 x^-5 + 32
C. f(x) = -28 x^-5 - 3
D. f(x) = -7 / 3 x^-3 + 13 / 3

Answer 1

To find f(x), we integrate f'(x) = 7 / x^4 and use f(1) = 4 to determine the constant of integration. The correct answer is D. f(x) = -7 / 3 x^-3 + 13 / 3.

Step-by-step explanation:

To find f(x) given f'(x) = 7 / x^4 and f(1) = 4, we can use the equation f(x) = ∫f'(x) dx. Integrating the given derivative, we get:

f(x) = -7 / 3x^3 + C

Substituting x = 1 and f(1) = 4, we can solve for C and find the final equation:

f(x) = -7 / 3x^3 + 13 / 3

Hence, the correct answer is D. f(x) = -7 / 3 x^-3 + 13 / 3.