The derivative of a function f with respect to x is given by (f'(x) = 3x^{2} – frac{4}{x^{5}}). If (f(1) = 4), find f(x).
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A.
(f(x) = x^{3} – frac{1}{x^{4}} + 2) -
B.
(f(x) = x^{3} + frac{1}{x^{4}} + 2) -
C.
(f(x) = x^{3} – frac{1}{x^{4}} – 2 ) -
D.
(f(x) = x^{3} + frac{1}{x^{4}} – 2)
Correct Answer: Option B
Explanation
(frac{mathrm d y}{mathrm d x} = 3x^{2} – frac{4}{x^5} = 3x^{2} – 4x^{-5})
(y = int (3x^{2} – 4x^{-5}) mathrm {d} x )
(y = x^{3} + frac{1}{x^{4}} + c)
f(1) = 4; (4 = 1^{3} + frac{1}{1^{4}} + c implies 4 = 2 + c)
(c = 2)
(f(x) = x^{3} + frac{1}{x^{4}} + 2)