Question

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

Options

• 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 \[x\in(c-h,c+h)\].

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

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

Answer 1

For a local maximum, \[f(c)\] is at least as large as nearby values of the function. The comparison is restricted to \[x\in(c-h,c+h)\], where \[h>0\].