Determine the intervals on which the function g ( x ) = 3 x 4 − 4 x 3 + 6 x 2 + 5 x + 1 g(x) = 3x^4 - 4x^3 + 6x^2 + 5x + 1 is concave up or concave down. Identify any inflection points.

Concave up on ( − ∞ , ∞ ) \left(-\infty,\infty\right) No inflection points

Concave up on ( − ∞ , 1 ) ∪ ( 1 , ∞ ) (-\infty, 1) \cup (1, \infty) Concave down on ( − 1 , 1 ) \left(-1,1\right) Inflection point at x = 1 x = 1

Concave down on ( − ∞ , ∞ ) \left(-\infty,\infty\right) No inflection points

Concave up on ( − ∞ , − 2 ) ∪ ( − 2 , ∞ ) (-\infty, -2) \cup (-2, \infty) Inflection point at x = − 2 x = -2

Determine the intervals on which the function g(x)...

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