Answer to Question #17680 in Calculus for hsd
Find the point(s) at which f achieves a local maximum.
Find the point(s) at which f achieves a local minimum.
Find the interval(s) on which f is concave up.
Find the interval(s) on which f is concave down.
Find all inflection points.
f''=-(72 (-1+x^2))/(3+x^2)^3 f"=0 iff x=1 or x=-1
x=0 we have local minimum because f'<0 if x<0 andf'>0 if x>0 there is no local maximumf">0 if x from(-1;1) so here f concave down
f"<0 at (-infinity;-1) and (1, infinity) so atthat interval it is concave up inflection points x=-1 x=1
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