Question

 ,

Given that y=37 at x=4, find y in terms of x, giving each term in its simplest form.

Solution

We are given that;

We are given coordinates of appoint that is y=37 at x=4 ie  (4,37).

We are required to find the equation of y in terms of x.

We can find equation of the curve from its derivative through integration;

Therefore,

Rule for integration of  is:

Rule for integration of  is:

If a point   lies on the curve , we can find out value of . We substitute values of  and    in the equation obtained from integration of the derivative of the curve i.e. .

Therefore, substituting the coordinates of point(4,37) in above equation;

Therefore, equation of the curve C is;