Question

Which statement gives the meaning of a local minimum at \[c\]?

Options

• \[f'(c)>0\] for all \[x\in(c-h,c+h)\].

• There exists \[h>0\] such that \[f(c)\leq f(x)\] for all \[x\in(c-h,c+h)\].

• There exists \[h>0\] such that \[f(c)\geq f(x)\] for all \[x\in(c-h,c+h)\].

• \[f(c)\leq f(x)\] for all \[x\] on the entire given interval.

Answer 1

For a local minimum, \[f(c)\] is no greater than the nearby values. The condition holds for all \[x\] in an interval \[(c-h,c+h)\] with \[h>0\].