Unformatted text preview: k ( x ) = exp (x T x ) is not. 4. Plot the function f ( x ) = cos ( 3 x ). 5sin ( 5 x )+ . 2cos ( 10 xπ / 4 ) . Estimate how many critical points it has on the interval [ , 2 π ] . Now consider g : R 20 → R given by g ( x ) = f ( x 1 ) f ( x 2 ) ··· f ( x 20 ) . Show that ∇ g ( x ) = is equivalent to f ( x i ) = 0 for all i . From this, estimate how many critical points g has in the cube [ , 2 π ] 20 . Clearly there is a potential to have many (irrelevant) local minima. Can you suggest ways of handling problems like this? 1...
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 Spring '12
 DavidStewart
 Critical Point, Optimization, Fermat's theorem

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