12. The width w of a rectangular swimming pool is 7x2. The area A of the pool is 7x3 – 42x2. What is an expression for the lengt
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, the second derivative is positive, indicating a relative MINIMUM.
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To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.
So minimize
Find the derivative of L and set it equal to zero.
This gives you
You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.
When x = 0, the second derivative is negative, indicating a relative maximum. When
The two points on the curve closest to the origin are