Calculating the critical points and sketching a function.

Let g(x) = 300-8x^3-x^4

-Find the local maximum and minimum values.
-Find the intervals of concavity and the inflection points.
-Use this information to carefully sketch the graph of g.

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...e down, (-4,0) is concave up, and (-oo, -4) is concave down.
(-1,307), (1,291), (10,-1500), (-8,300), and (3,3) are points on the graph as well
Note: There is an iterative way to find the two x intercepts exactly, but for this graph, you just have to estimate the two values.
A general description ...