Find the absolute maximum and minimum values of the function f(x, y) = x2 + xy + y2 on the disc x2 + y2 ≤ 1. (you do not have to use calculus.)

The required  absolute maximum and minimum values of the function is 0 and .

Given that,

Function on disc .

We have to determine,

The absolute maximum and minimum values of the function.

According to the question,

Consider the polar points,

The equation of the circle,

Then, (x, y) can be written as,

Therefore,   which means they share the same extreme values.

Over the disk, points lies

Where, r = 0 then

And Where r = 1 then,

When

Then,

Along the boundary we get

Therefore, f(x, y) has a minimum value of 0 and a maximum value of over the unit disk .

Hence, The required  absolute maximum and minimum values of the function is 0 and .

For more information about the Maxima and Minima click the link given below.

link

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step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: