Calculus, 8th Edition,stewart; page 34 problem 11

Question

Find an expression for a cubic function f if f (1) = 6 and f (-1) = f (0) = f (2) = 0.

Answer 1

Step:1

The functions are  and .

Here  are the zeros of .

If  then  is a factor of .

If  then  is a factor of .

If  then  is a factor of .

The cubic function is in the form of , where  are zeroes of the function.

                      (1)

Step:2

.

The function  at  is .

Substitute  and  in equation (1).

Substitute  in equation (1).

The cubic function is .

Solution:

The cubic function is .