Suppose f(x,y)=(x-y)(16-xy). Answer the following 1. Find the local maxima of

percibaa8 2021-12-20 Answered
Suppose \(\displaystyle{f{{\left({x},{y}\right)}}}={\left({x}-{y}\right)}{\left({16}-{x}{y}\right)}\). Answer the following
1. Find the local maxima of \(\displaystyle{f}\).
2. Find the local minima of \(\displaystyle{f}\).
3. Find the saddle points of \(\displaystyle{f}\).

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

lalilulelo2k3eq
Answered 2021-12-21 Author has 2501 answers
\(\displaystyle{f{{\left({x},{y}\right)}}}={\left({x}-{y}\right)}{\left({16}-{x}{y}\right)}\)
\(\displaystyle{f}_{{x}}={\left({16}-{x}{y}\right)}+{\left({x}-{y}\right)}{\left(-{y}\right)}={16}-{x}{y}+{y}^{{2}}-{x}{y}\)
\(\displaystyle{f}_{{y}}={\left({x}{y}-{16}\right)}+{\left({x}-{y}\right)}{\left(-{x}\right)}={x}{y}-{16}-{x}^{{2}}+{x}{y}\)
\(\displaystyle{f}_{{x}}={0}\ \Rightarrow\ {y}^{{2}}-{2}{x}{y}-{16}={0};\ \Rightarrow{y}^{{2}}={x}^{{2}}\)
\(\displaystyle{f}_{{y}}={0}\ \Rightarrow\ {x}^{{2}}-{2}{x}{y}-{16}={0};\ \Rightarrow{y}=\pm{x}\)
\(\displaystyle{y}={x}\ \Rightarrow\ {x}^{{2}}-{2}{x}^{{2}}+{16}={0}\ \Rightarrow\ {x}^{{2}}={16}\ \Rightarrow\ {x}=\pm{4}\)
\(\displaystyle{y}=-{x}\ \Rightarrow\ {x}^{{2}}+{2}{x}^{{2}}+{16}={0}\ \Rightarrow\ {x}^{{2}}=-{\frac{{{16}}}{{{3}}}}\) - not possible
\(\displaystyle{\left({x},{y}\right)}={\left(-{4},-{4}\right)},{\left({4},{4}\right)}\)
\(\displaystyle{f}_{{\times}}=-{2}{y};\ {f}_{{{y}{y}}}={2}{x};\ {f}_{{{x}{y}}}=-{2}{x}+{2}{y}\)
\(\displaystyle{D}=-{4}{x}{y}-{4}{\left({x}-{y}\right)}^{{2}}\)
\(\displaystyle{D}{\left({4},-{4}\right)}=-{4}{\left({16}\right)}=-{64}{ < }{0}\)
\(\displaystyle{D}{\left({4},{4}\right)}=-{4}{\left({16}\right)}=--{64}{ < }{0}\)
Not exactly what you’re looking for?
Ask My Question
0
 
psor32
Answered 2021-12-22 Author has 2040 answers
Concretise the answer, please
0
nick1337
Answered 2021-12-28 Author has 9672 answers
1) none

2) none

3) (-4,-4,0), (4,4,0)
0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-23

Find the limit (if it exists) and discuss the continuity of the function.
\(\lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-z}\)

asked 2021-09-18
Find the limit and discuss the continuity of the function. \(\displaystyle\lim_{{{x},{y}}}\rightarrow{\left({\frac{{\pi}}{{{4}}}},{2}\right)}{y}{\cos{{x}}}{y}\)
asked 2021-09-11
Rectangular equation is xy=5. Transform it into polar equation.
asked 2021-09-15
If \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{2}{x}-{x}^{{2}}}}\) , graph the following functions in the viewing rectangle [-5,5] by [-4,4] . How is each graph related to the graph in part (a)?
asked 2021-06-14

Describe the transformations that must be applied to \(y=x^2\) to create the graph of each of the following functions.
a) \(\displaystyle{y}=\frac{{1}}{{4}}{\left({x}-{3}\right)}^{{2}}+{9}\)
b) \(\displaystyle{y}={\left({\left(\frac{{1}}{{2}}\right)}{x}\right)}^{{2}}-{7}\)

asked 2021-08-14
Suppose you take a dose of m mg of a particular medication once per day. Assume f equals the fraction of the medication that remains in your blood one day later. Just after taking another dose of medication on the second day, the amount of medication in your blood equals the sum of the second dose and the fraction of the first dose remaining in your blood, which is m+mf. Continuing in this fashion, the amount of medication in your blood just after your nth does is \(\displaystyle{A}_{{{n}}}={m}+{m}{f}+\ldots+{m}{f}^{{{n}-{1}}}\). For the given values off and m, calculate \(\displaystyle{A}_{{{5}}},{A}_{{{10}}},{A}_{{{30}}}\), and \(\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}\). Interpret the meaning of the limit \(\displaystyle\lim_{{{n}\rightarrow\infty}}{A}_{{{n}}}\). f=0.25,m=200mg.
asked 2021-09-23
Find domain of fog, if
1. \(\displaystyle{f{{\left({x}\right)}}}={x}+{5};{g{{\left({x}\right)}}}=\frac{{7}}{{{x}+{7}}}\)
2. \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{x}};{g{{\left({x}\right)}}}={6}{x}+{18}\)
...