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This gets difficult to explain on paper, if you are stuck with my explanations, feel free to write your thoughts here.

Date Posted:
4 months ago

Since the inflection is (0, 5) and the MINIMUM point is (1, 4), the graph will never cut the x-axis.

Since there are only two stationary points, the curve will never ever go down again after x = 1.

For a positive x^4 graph, the graph starts out going down.

Inflection points work in a similar way.