Unfinished Math Notes
2
Optimization: For Abs. Max and Min for F over a region S: 1. Identify x 0 where ∇ f ( x 0 ) = 0, x 0 should be ∈ S 2. Find critical points along the curve formed b boundar of S !. "se a table and compare functions of points from #1$ and #2$ and determine max%min. &onstraint 'rocess: (xample: )et f ( x , y , z ) = y 2 − z − x ∇ ( f , x , y , z ) = ( − 1,2 y , − 1 ) , ∧ therefore≠ 0 *o+ever, +e can constrain the general function b putting the curve into an outer function Let domain of f ( x , y , z , ) the value given by g ( t ) =( t , t 2 , t 3 ) 'ut the inner curve into the outer. H ( t ) = t 4 − t 3 − t H ' ( t ) = 4 t 3 − 3 t 2 − 1 Find the critical point: t-1 Second erivative /est: 0f critical point that is plugged in is positive , then the function has a relative minimum at the point if critical point that is plugged in is negative , then the function has a relative maximum at the point. H ' ' ( t ) = 12 t 2 − 6 t
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Transcript of Unfinished Math Notes
Optimization:For Abs. Max and Min for F over a region S:1. 2. Find critical points along the curve formed by boundary of S3. Use a table and compare functions of points from (1) and (2) and determine max/min. Constraint Process:Example: Let
However, we can constrain the general function by putting the curve into an outer function
Put the inner curve into the outer.
Find the critical point: t=1Second Derivative Test: If critical point that is plugged in is positive, then the function has a relative minimum at the point; if critical point that is plugged in is negative, then the function has a relative maximum at the point.
