Find the critical point of the function

Maggie.D just a moment. 0 answers, 0 views
calculus multivariable-calculus

Consider the following function.

$g(x, y)=e^{−8x^2−6y^2+24y}$

(a) Find the critical point of g.

(b) Using your critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point.

(c) Use the Second Partials test to classify the critical point from (a).

For C, the options are either

Saddle Point, Relative Minimum, Relative Maximum, or Inconclusive

I could really used some help finding the critical point. I separated them into $f_x$ and $f_y$ and set them equal to 0 and got (24,0). I'm not sure if this answer is right and what I am supposed to do to find b.

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