Please please help with this question!!?

Question

If a continuous function f(x) has a local maximum at x = c, then which of the following statements is false?

a) (c, f(c)) is a critical point
b) f(x) changes from increasing to decreasing at x = c
c) f(x) changes from positive to negative at x = c
d) f(x) changes from changes from concave down to concave up at x = c

Answer 1

c is false. it's f'(x) that changes + to - at a local max.

d is false. f(x) is concave down in the neighborhood of a local max.