Question

What is the upper bound of the function? f(x)=2x^4−5x^2−45x−3 Enter your answer in the box.

upper bound = __

I don't know but I got 4 and I want to be sure.

Answer 1

upper bound = __4

Explanation:

The upper bound is found out by doing synthetic division and if we get the answer(all values) positive then that integer is said to be the upper bound.

Lets start with 1

1 { 2 0 -5 -45 - 3}

2 2

2 2 -3 end

Now do with 2

2 { 2 0 -5 -45 -3 }

2 4

2 2 -1 end

Using 3

3 {2 0 -5 -45 -3 }

6 18 39

2 6 13 - 6 end

Solving with 4

4 { 2 0 -5 -45 -3 }

8 32 108 252

2 8 27 63 249

So only 4 gives the positive values at the bottom line.

Hence x = 4 is the upper bound