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Problem 975

Determine the critical points of $\mathrm{f}(\mathrm{x})=3 \mathrm{x}^{4}-4 \mathrm{x}^{3}$ and sketch the graph.

Expert verified

The critical points of the function \(f(x) = 3x^4 - 4x^3\) are \(x = 0\) (inflection point) and \(x = 1\) (local minimum). The graph starts at a positive value, decreases to a local minimum at \(x = 1\), and then increases indefinitely.

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