The following statements are either true or false.
a). If x=p is not a critical point of f, then x=p is not a local maximum of f.
b). If x=p is not a local maximum of f, then x=p is not a critical point of f.
c). If f'(x) is continuous and f(x) has no critical points, then f is everywhere increasing or everywhere decreasing.
d). If f''(x) is continuous and the graph of f has an inflection point at x=p, then f''(p) = 0.
a) true - all local maximums are critical points
b) false - a critical point can also occur at the ...
This shows how to determine if a set of statements regarding calculus functions are true or false.