concave up or concave down?

[zebra]

f(x)=x^3-2x^2+x+1

how do u find intervals on which the graph of f is concave upward or is concave downward? the Point of Inflection is 2/3

 

[skeeter]

set f"(x) = 0, solve for x.

check a value of f"(x) on either side of the critical value found above ...
if f"(x) < 0, f(x) is concave down
if f"(x)> 0, then f(x) is concave up

btw ... x = 2/3 is a point of inflection only if f"(x) changes sign there.

 

[zebra]

thanks that was very helpful...i was trying to check for values of f'(x). it just wasnt working