97.7k views
3 votes
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

User Kunal Jha
by
8.6k points

1 Answer

3 votes

Final answer:

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.

User Saumil Gauswami
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories