Question

 ,

a.   Show that

Where A and B are constants to be found.

b.   Find

Given that the point (-3,10) lies on the curve with equation y=f(x),

c.   Find f(x).

Solution

a.
 

We are given;

Therefore;

b.
 

We are given;

We are required to find .

Second derivative is the derivative of the derivative. If we have derivative of the curve   as  , then  expression for the second derivative of the curve  is;

Therefore, for the given case;

As demonstrated in (a);

Therefore;

Rule for differentiation is of  is:

Rule for differentiation is of  is:

Rule for differentiation is of  is:

c.
 

We are given coordinates of a point on the curve (-3,10).

We are required to find the equation of y in terms of x ie f(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(-3,10) in above equation;

Therefore, equation of the curve C is;