The lateral area of a cube is 36 Square inches. How long is each edge?
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Answer:
The minimum surface area of the container is 276.791 square units.
Step-by-step explanation:
Let be ,
,
. The first and second derivatives of such function are, respectively:
First derivative
Second derivative
The critical values of are determined by equalizing first derivative to zero and solving it: (First Derivative Test)
(since radius is a positive variable)
To determine if critical value leads to an absolute minimum, this input must be checked in the second derivative expression: ()
The critical value leads to an absolute minimum, since value of the second derivative is positive.
Finally, the minimum surface area of the container is:
The minimum surface area of the container is 276.791 square units.
<h2><u>Answer:</u></h2><h2><u>1. 2x⋅(2x+1)</u></h2><h2><u>2. −2</u>
</h2><h2>3. −1⋅(x+6)</h2>