Question

when finding the second derivative to test concavity, do you only set the numerator equal to 0 or do you also set the denominator equal to 0? (when the second derivative is not defined?)

Answer 1

the concavity is given by:
1. second order derivative < 0 - this implies concave up
2. second order derivative > 0 - this implies concave down
3. second order derivative = 0 - this implies you have a point of inflection

when you get a fraction equal to zero, e.g.:\[\frac{3x+2}{7x^2-1}=0\]then you only consider the numerator.