@acer 

The green points are the saddle points and drawing two levelcurves there shows exactly what characterise these saddle points

@acer 

Thanks

For a procedure to make there is the function itself and the domain to specify as input 
So a message : enter function and domain.
For educational purpose : showing the steps in the calculation as a list 
Showing in the critical points the two tangentlines and  levelcurves

Also interesting is to go  further with a plot of two functions also in a procedure and do something with a gradient and level curves

@Kitonum 

Thanks

Its good to know in your worksheet how those critical points are named.
And there is are locals points  and  more.

@Rouben Rostamian  
Thanks
There are for sure 6 points, but we don't nothing yet about the sadlepoints.
Perhaps later adding some more plots in one view to get the whole picture of

For now i look in old studymaterial how the questions were formulated.

@nm 
Thanks

Looks good to read!
The axis need also a symbol 
Comes later..

Taking_a_list_of_numeric_values_L.mw

@acer 
Thanks

[[0, f(0)], [Pi/6, f(Pi/6)], [Pi/4, f(Pi/4)], [Pi/3, f(Pi/3)], [Pi/2, f(Pi/2)]]

this is a list of lists of sin(x), without the functionvalues, but when i do want this list? 

@Kitonum 

Thanks, its clear

@Carl Love 
Thanks

I am looking to the upgrade of the AMD ryzen 6 core processing and further i found..

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AMD Ryzen 5 1600 offers 9% more performance per watt. Specifications: The AMD Ryzen 5 1600 has a thermal design power (TDP) of 65 Watts; The Intel Core i7-6850K, Intel’s lowest-power 6-core processor, has a thermal design power (TDP) of 140 Watts. Performance may vary based on use of latest drivers. RZN-37
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That TDP of 65 Watts is really good for the energyconsumption and reliability of the computerssytem..too much heath is a problem for the electronics as i know from my own experience.

@janhardo 

CPU and internal memory are important for computer speed, and it seems that the SDD only is for starting up the system as i have informed at the computerstore.

@janhardo 

Well,were is the next prime is be answered in this article : Where is the next Mersenne prime? (utm.edu)
Some statistics used to predict the gap between the known 51 mersenne prime and the following unknown 52 mersenne prime 
This 52 mersenne prime quess can be a prime or not  

Quote :
So what can we gather from this?  One thing is that given one Mersenne prime exponent's p, the next one will fall, on the average, near 1.47576p.  But not too near the average much of the time--sometimes the gaps will be small, sometimes large.  So the next larger Mersenne exponent might be over 85,000,000 yielding a Mersenne with nearly 26 million digits.  Or it may not.

Mersenne prime 51 = 82,589,933 x 1,47576 = 121.882.919,5 (mersenne prime 52 expected on average 
But is it not that the gaps between mersenneprimes becomes larger and larger direction infinity, but we are now here on mersenne prime of p= 85 million to start with the search 
Don't know how they it doing on the GIMPS website with there search?

@Carl Love 

Looks like the internal computer memory is not a bottle neck for speed, so a fastest SDD drive on a motherboard can increase speed of calculations.
Wonder if the search to a bigger prime is not done by a supercomputer ?

12 Fastest Supercomputers In The World | In 2021 - RankRed

How do they do it on the GIMPS website ?

@janhardo 

A external sdd drive is  plug and play goes to 2000 Mb/s for reading /writing for all models
The motherboard ssd's  are much faster and cheaper but must be built in, but it is not big deal

@acer 

Thanks

Probably i change  something in the  Tools->Options->Display 
Its now working again.

@janhardo 

Can i go reverse ..and  express 10^ 24,862,048 as mersenne exponent prime ?
1,39822 x 10^316 could be  a mersenne prime or not ? 
In general ,how to search from the latest found primenumber further: what number to take as next one ?
Mp = 2^(last one +1) - 1 ..no estimation for this ?

The next Mersenne prime will be about 2x times bigger then his precessor
example : 2^4 ( forget this -1)  =   2^3 -1 x 2^1 , but calcualtion time is not doubling as  two calculation has shown for two mersenne primes and it doesn't matter for CPU speed, i think, it all goes now faster with the same speed ratio's in time.
Its a exponential curve 2^x ..