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Is increasing Average Product(AP) always implying increasing Marginal Product(MP) in microeconomics?

Consider the following production function: $f(x)=\begin{cases} x^2 & x < 1 \\ x^{\frac{3}{2}} & x \geq 1\end{cases}$ In this case, the average product is $\text{AP}(x)=\dfrac{f(x)}{x}=\...
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