For , let . Determine all –values at which has an inflection point, and justify your…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For

x\neq0

, let

f'(x)=\dfrac{x^{2}-4}{x^{2}+1}

. Determine all

x

–values at which

f

has an inflection point, and justify your conclusion by analyzing concavity on the intervals determined by those values.