I have u(x,t)=-2xt-x^2 find maximum in region {-2 ≤ x ≤ 2 , 0 ≤ t ≤ 1}(adsbygoogle = window.adsbygoogle || []).push({});

I believe to find the critical point first I have to take the partial derivative with respect to x and t and equate to zero.

Thus

Ux=-2t-2x = 0

Ut=-2x = 0

Thus the only critcal point I find is x=0, t=0.

But the maximum (answer at back of book) is x=-1, t=1 => u(-1,1)=1

Where did I go wrong?

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# Maximum of a function u(x,t)

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