QuestionDecide which function is an antiderivative of the other: $$f(x)=\frac{5}{\sqrt{x}} \quad g(x)=10 \sqrt{x}$$
Choose one

Studdy Solution
Compare the antiderivatives:
The antiderivative of $f(x) = \frac{5}{\sqrt{x}}$ is $10\sqrt{x} + C$, which matches $g(x)$.
The antiderivative of $g(x) = 10\sqrt{x}$ is $\frac{20}{3}x^{3/2} + C$, which does not match $f(x)$.
Therefore, $g(x) = 10\sqrt{x}$ is an antiderivative of $f(x) = \frac{5}{\sqrt{x}}$.
The function $g(x) = 10\sqrt{x}$ is an antiderivative of $f(x) = \frac{5}{\sqrt{x}}$.