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Fed [463]
3 years ago
9

Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

Mathematics
1 answer:
slavikrds [6]3 years ago
8 0
f'(x)=2x-\dfrac3{x^4}
\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx
f(x)=x^2+\dfrac1{x^3}+C

Given that f(1)=2, we get

2=1^2+\dfrac1{1^3}+C
2=2+C
\implies C=2

so that

f(x)=x^2+\dfrac1{x^3}
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