## Related questions with answers

Question

Find the local maximum and minimum values and saddle point(s) of the function. If you have three - dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function.

$f(x, y) = x^3 - 3x + 3xy^2$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 5We can find the local extrema using the Second Derivatives Test from the section. Note that

$f(x,y)=x^3-3x+3xy^2$

is a polynomial function (in 2 variables) and hence is continuous everywhere in its domain. Thus the theorem applies.

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