Question: Let f(x) = a 0 +a 1 x+a 2 x 2 , a 2 0, be a quadratic function and g(x) = b 0 +b

Let f(x) = a0+a1x+a2x2, a2 0, be a quadratic function and g(x) = b0+b1x+b2x2+b3x3, b3 0, be a cubic polynomial.

1. Prove that f(x) will always be either concave up or concave down.

2. Prove that g(x) must have exactly one inflection point.

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