Question

K=1; f(x)=4x^3-2x^2+2x+4; Lower bound?

Answer 1

Given:
$f(x) = 4x^{3} - 2x^{2} + 2x + 4$
and,
K = 1

We would require to do the synthetic division of the above problem in order to know whether K=1 is a lower bound or not. Let's do it!

Steps of Synthetic Division:

1. Write the coefficients of the equation, and before that write 1. Like,

1 ║ 4   -2   2   4

As you can see, the coefficients of the equation are seperated by ║.

2. Drop down the first value after ║as it is. Like:
1 ║ 4   -2   2   4
        :
----------------------
       4

3. Multiply 4 with 1 and then  place the resultant value under -2 and then add that resultant value with -2. Like
1 ║ 4   -2   2   4
        :    4
----------------------
       4   2

4. Repeat Step 3 until you're done.

1 ║ 4   -2   2   4
        :    4   2   
----------------------
       4   2    4   

1 ║ 4   -2   2   4
        :    4   2   4
----------------------
       4   2    4   8


Now every value, +4, +2, +4, +8, under the bar(---------) is positive; therefore, it means that K=1 is the upper bound, NOT lower bound.

Ans: K=1 is NOT a lower bound.
-i