f(æ, y) = ry(1 – 6x – 5y)has 4 critical points. List them and select the type of critical point.Points should be entered as ordered pairs and listed in increasing lexicographic order. By that we mean that (, y) comes before (z, w) if z <z or if z = z and y < w.First point (0,0)of type SaddleSecond pointof type ?Third point (1/18,1/15)of type Maximum vFourth pointof type ?

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Asked Dec 19, 2019
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f(æ, y) = ry(1 – 6x – 5y)
has 4 critical points. List them and select the type of critical point.
Points should be entered as ordered pairs and listed in increasing lexicographic order. By that we mean that (, y) comes before (z, w) if z <
z or if z = z and y < w.
First point (0,0)
of type Saddle
Second point
of type ?
Third point (1/18,1/15)
of type Maximum v
Fourth point
of type ?
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f(æ, y) = ry(1 – 6x – 5y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that we mean that (, y) comes before (z, w) if z < z or if z = z and y < w. First point (0,0) of type Saddle Second point of type ? Third point (1/18,1/15) of type Maximum v Fourth point of type ?

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Expert Answer

Step 1

For the given function all its first and second derivatives are calculated as.

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f-у-12ху - 5у 5, 3х- бх* - 10ху =-12y хх -10х yy S, 3Sn 3D1-12х- 10y ху ух

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Step 2

Now finding the critical points using the first derivative and put it to zero. These can be determined using trivial methods in this case as.

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f, = 0 5y – y (1–12x) = 0 x = 0 5y² – y = 0 y = 0,-

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Step 3

And also for the derivative with respect to ‘y’ put i...

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f, = 0 6x² – x (1–10y) = 0 y = 0 6x? – x = 0 x = 0, (0.0) (0)(0 |are critical pts.

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Calculus