Let g be a function defined and continuous on the closed interval [a,b].

Question

Let g be a function defined and continuous on the closed interval [a,b]. If g has a relative minimum at c and a < c < b , which of the following statements must be true?

i. g' (c) exists

ii. g' (c) exists, then g' (c) = 0

iii. If g" (c) exists, then g" (c) ≤ 0

Answer 1

The only correct statement is ii. That is, if the derivative at c exists then it must be 0 since c must be a critical point of the function g.