Subject: Math problem!

To find local extreme values you have to use partial differentiation. That gives:

d/dx T(x,y,z) = z
d/dy T(x,y,z) = 2y
d/dz T(x,y,z) = x

A necessary condition for a point (a,b,c) to be an extreme value of T is, that all partial derivatives vanish. That is only fulfilled by one point. You have to check now if that point is really an extreme value and if it is not one, where would you find the extreme value then, if not by partial differentiation?

For discussing extremes in multivariate calculus, you should consult Hessian matrix, though I can't say you more now as I have forgotten the details...

You would check if the Hessian matrix is positive or negative definite or indefinite, but actually in this case you can see it in a more 'natural' way.

The only point that could be a local extreme value is (0,0,0). The Hessian Matrix in this point is

0 0 1
0 2 0
1 0 0

which is indefinite (it has eigenvalues 1, 2 and -1). So (0,0,0) is not an extreme value.

A more natural approach: If you start at the point (0,0,0), then the function T takes the value 0. If you let x and z tend a little towards a positive value each, then the function T gets positive. If you let z tend to a negative value instead then T gets negative. Therefor (0,0,0) can't be an extreme value, since there are points who's values under T are bigger and points who's values under T are smaller than 0 in every Neighbourhood of (0,0,0).

Since there is no local extreme value, the function takes its maximum and its minimum on the boundary. So you have this problem

max/min y^2 + xz

under the condition: x^2 + y^2 + z^2 = 1

try transforming into spherical coordinates;)

can someone help me with this

it seems so easy but I dont have idea how to start :D

(10^2log3) = 8x+5

It's a linear equation in x, so isolating x gives:

x = [ (10^2log3) - 5 ] / 8

maybe you want to rewrite the exponential-term with the logarithm? I don't see anything else what you can do with that equation ;)

I have to get that x=1/2

but dont really know how :/

With 'log' you mean log to base 10 ?

Then you get with some logarithm rules:

10^2log3 = 10^log(3^2) = 10^log9 = 9

and so

9 = 8x + 5

which has the solution x=1/2

thanks :)

I need help again

how to solve this:

[((2(x-y)^2)^2)^6 + ((2(x-y)^4)^2^)^3] / 65

x=4
y=2

the result should be 2^26

I tried something and got (8^12 + 32^6)/65 but what to do after that...
(edited)

8^12=2^36
32^6=2^30

(2^36+2^30)/65=2^30*(2^6+1)/65=2^30

thx

I hope its correct :)

it's correct

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is anybody here, who could help me with some Geometry?

level: university

just to give me some tips and directions how to solve stuff

I'm not a geometry specialist, but I'm doing my Math PhD, so maybe I can help ;-)