Intervals of concavity and inflection point(s)?

[stinajeana]

I need help with these 2 questions which involve finding the intervals of concavity and inflection points:

1. f(x)= ((x^4)-(8x^2)-9) / (x-3)(x+3) [x^2+1]

2. g(x)= ((x^2)+(2x)-15) / ((x^2)+(2x)-3


Please guide me? I have no idea where to start

 

[DrPhil]

I need help with these 2 questions which involve finding the intervals of concavity and inflection points:

1. f(x)= ((x^4)-(8x^2)-9) / (x-3)(x+3) [x^2+1]

2. g(x)= ((x^2)+(2x)-15) / ((x^2)+(2x)-3.....Need closing ")"?


Please guide me? I have no idea where to start

Curvature is given by the second derivative. If positive, the curve is concave up. If negative, concave down. Inflection points occur where the numerator is zero - but the curvature may also change at points where the 2nd derivative does not exist.