Hi, help with question 18 please. thanks​

See Below.

Step-by-step explanation:

We are given the equation:

And we want to prove that:

Find the first derivative by taking the derivative of both sides with respect to x:

Divide both sides by 2y:

Find the second derivative using the quotient rule:

Substitute:

Simplify:

Combine fractions:

Simplify:

Cancel:

Substitute:

Simplify. Hence:

Q.E.D.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: