Question

please help :)
For the polynomial, f(x)=1-2x+5x^4 as x---> infinity, f(x) ---> -infinity

true or false?

Answer 1

I would suggest plugging in a few values of x and testing it.

Try x = 100, x = 1000, and x = 10,000.
You should then be able to make a very good guess at the answer. :)

Answer 2

Basically, we are making x go toward infinity and we want to see how the formula responds, does it seem to be getting bigger (and heading toward + infinity)? Or does it seem to be getting really big in a negative direction (and heading toward - infinity)?

Answer 3

I think it's false?

Answer 4

I would agree! The values just keep getting bigger, and Bigger, and BIGGER! And they always stay positive.

Even though there is a -2x in our formula the 5x^4 is just too powerful and forces the function to stay positive. Nice work!

Answer 5

thanks for your help!! :)

Answer 6

Your welcome!