(Solved): Mang Gustin observed that when he uses \( x \) units of fertilizer, he is able to yield \( m(x)=-\ ...

Mang Gustin observed that when he uses \( x \) units of fertilizer, he is able to yield \( m(x)=-\frac{1}{4} x^{4}+4 x^{3}-22 x^{2}+48 x-30 \) thousand kilograms of mangosteen. How many units of fertilizer must he use to obtain a maximum yield if he is required to use at least 1 unit but not more than 5 units of fertilizer? Verify your answer by sketching the graph of \( m \). Show your complete solution.