## Related questions with answers

Question

Find a function y=f(x) that satisfies both conditions: $\frac{d y}{d x}=3 x^{-1}-x^{-2} \quad f(1)=5$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Let's integrate derivative from the exercise to find $y=f(x)$.

$\begin{aligned} y&=\int\dfrac{dy}{dx}dx\\ &=\int(3x^{-1}-x^{-2})dx\\ &=3\ln|x|-\dfrac{x^{-1}}{-1}+C\\ &=3\ln|x|+\dfrac{1}{x}+C \end{aligned}$

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