# Got a question with substitution?

• MRAI
In summary, the conversation discusses finding the maximum value of a quadratic equation using the Substitution method. It is recommended to complete the square to find the vertex of the graph, which gives the maximum value. Another method, discovered by Lagrange, may be more elegant but requires a higher level of mathematical knowledge.
MRAI
Using the Substitution method, find the maximum value of

4x-2xy+3y subject to the constraint 4x-y=2

I can do the 1st part:

4x-y=2--->
4x-2=y

substitute this into the original equation:
4x-2x(4x-2)+3(4x-2)

Hope that right so far! but don't know where to go from there? anyone could help please?

thanks ;)

then you differentiate wrt x and equal to zero to find max/min

what do u mean by wrt?

"wrt" : "with respect to"
CartoonKid was assuming this was a calculus problem. The standard method for solving "maximum- minimum" problems in calculus is to differentiate and set the derivative equal to 0. But since you apparently weren't aware of that, I suspect this is not a calculus problem!

If you multiply y= 4x-2x(4x-2)+3(4x-2) out, you get a quadratic. If you are doing problems like this, I presume you know how to complete the square to find the vertex of the graph which, in this problem, gives you the maximum value.

So: multiply this out, then complete the square.

This method is totally counterproductive...The method discovered by Lagrange is much more elegant...

Daniel.

But one would need a rather intermediate mathematical background to use them...

## 1. What is substitution in science?

Substitution is a term commonly used in chemistry and refers to the replacement of one atom or group of atoms with another in a chemical compound. This process can result in a new compound with different properties than the original one.

## 2. What are some examples of substitution reactions?

Some common examples of substitution reactions include the replacement of a hydrogen atom with a halogen atom in an alkane, the replacement of a hydroxyl group with a halogen atom in an alcohol, and the replacement of a hydrogen atom with a functional group in an organic compound.

## 3. How does the substitution reaction mechanism work?

In a substitution reaction, the original molecule or compound is called the substrate and the replacing atom or group is called the substituent. The substitution reaction involves breaking the bond between the substrate and a specific atom or group, and forming a new bond with the substituent.

## 4. What are the factors that affect substitution reactions?

The rate of substitution reactions can be influenced by a variety of factors, including the nature of the substrate and substituent, the presence of a catalyst, and the reaction conditions such as temperature and pressure.

## 5. How is substitution used in industries?

Substitution reactions are widely used in industries for the production of various products, such as plastics, pharmaceuticals, and agricultural chemicals. These reactions can also be used to modify existing compounds and create new ones with desired properties. Additionally, substitution reactions play a crucial role in organic synthesis and drug discovery processes.

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