Question

Find all values of x such that f(x)>0 and f(x)<0. f(x)=x^4+3x^3-4x^2

Answer 1

\[f(x)=x^4+3x^3-4x^2=x^2\left(x^2+3x-4\right)=x^2(x+4)(x-1)\]
This should help to see when \(f(x)\) is negative/positive.

Answer 2

I factored it to x^2(x+4)(x-1). Does that make my x intercepts (-4,0),(1,0) is the correct?

Answer 3

You're missing one, \((0,0)\).

Answer 4

Now you just test some \(x\) values in the intervals
\[(-\infty,-4)\\
(-4,0)\\
(0,1)\\
(1,\infty)
\]

Answer 5

Thank you, very helpful 😄

Answer 6

You're welcome