The graph of the polynomial f(x)= 3x⁴ - 4x³ is in the image at the end.
How to sketch the graph of the polynomial?
Here we have the polynomial:
f(x)= 3x⁴ - 4x³
Notice that we can rewrite this polynomial as:
f(x)= x³(3x - 4)
First, notice that when x = 0 we have:
f(0) = 0³*(3*0 - 4) = 0
We have a root here with multiplicity of 3.
Also, when:
(3x - 4) = 0
We have the other root.
3x = 4
x = 4/3
So:
f(4/3) = 0
At the moment we have two roots (0, 0) and (4/3 ,0)
Finally, also we can notice that the degree is even (it is 4), and the leading coefficient is positive (it is 3)
Which means that the end behavior is:
x → ∞, f(x) →∞
x → -∞, f(x) →∞