List all the 4-digit even numbers that can be created by rearranging these number tiles.
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Answer:
Step-by-step explanation:
Expression for the rectangular area and perimeter are, respectively:
After some algebraic manipulation, area expression can be reduce to an one-variable form:
The first derivative of the previous equation is:
Let the expression be equalized to zero:
The second derivative is:
According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:
The maximum area is: