Question

Find all values of x such that f(x)>0 and all x such that f(x)<0, and sketch the graph of f.

\[f(x)=\frac{1}{4}x^3-2\]

Answer 1

Do I just express the function as an inequality and solve?
\[\frac{1}{4}x^3-2 > 0\]
and \[ \frac{1}{4}x^3-2 < 0\]

Answer 2

You bet!

Answer 3

How do I solve this: (x-2)(x^2+2x+4)>0

I know that one of the zero's is 2...but...

Answer 4

When you can't factor you have to use the quadratic formula, and as there are no two numbers who add to positive 2 and have 4 as a product, we will have to use it here.

Answer 5

But then I get complex solutions... do I just ignore it?

Answer 6

As best as I understand, yes. Also, if you have a graphing calculator handy you will see that the only x intercept is in fact 2.

https://www.google.ca/webhp?sourceid=chrome-instant&ie=UTF-8&ion=1#hl=en&sclient=psy-ab&q=(1%2F4)(x%5E3)-2&oq=(1%2F4)(x%5E3)-2&aq=f&aqi=g-bCK4&aql=&gs_l=hp.12..0i8i33i30l4.0.0.1.3275.0.0.0.0.0.0.0.0..0.0...0.0.M63UOcty56w&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&fp=29d5eb6803e10871&ion=1&biw=1745&bih=880

Answer 7

I am not allowed to use a graphing calculator nor do I own one. Nevertheless, Thanks so much for all your help I really do appreciate it :).

Answer 8

No worries :)