Question

Graph each function considering the domain, critical points, symmetry regions, where the function is increasing or decreasing, inflection points where the function is concave up or down, intercepts where possible and asymptote where applicable f(x)= x^4- 4x^3/3- 4x^2 +1

Answer 1

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Answer 2

I assume, but cannot be sure, that you meant

f(x) = (x^4-4x^3)/(3-4x^2) + 1

since 3-4x^2+1 is kind of pointless.

The denominator is zero when x = ±√3/2, so that is where the vertical asymptotes are.

Before going any further, it'd be nice to know whether my f(x) is right. At any rate, recall that

f(x) is increasing where f'(x) > 0
f(x) is concave up where f"(x) > 0

and so on. I can reiterate all the useful info here, but I'm sure it's summarized in shaded boxes in your text.

If you still need help, maybe you could come up with f' and f", and then we can apply that information to answering the questions asked above.