OpenStudy (anonymous):

(1) the graph of every cubic polynomial has precisely one point of inflection (2) f''(2)=0 then the graph of f must have a point of inflection at x=2 (3) If f ' (c)>0 then f is concave upward at x=c

4 years ago
OpenStudy (anonymous):

anyone?!

4 years ago
OpenStudy (sirm3d):

(1) TRUE. the second derivative of a cubic polynomial is a linear polynomial, which has exactly one root, implying exactly one point of inflection.

4 years ago
OpenStudy (sirm3d):

(2) generally FALSE. the first derivative locates the relative maximum or minimum, or a horizontal tangent line. special case when it is true. f(x) = (x-2)^n for integers n=3,4,5,...

4 years ago
OpenStudy (sirm3d):

(3) FALSE. the first derivative desribes whether the graph is rising (f'(c) > 0) or falling (f'(c) < 0)|dw:1354710124564:dw|

4 years ago