ka1leE

2021-06-12

Explain the difference between an absolute minimum and a local minimum.
1) There is no difference.
2) A function f has an absolute minimum at $x=c$ if $f\left(c\right)$ is the smallest function value on the entire domain.
3) A function f has an absolute minimum at $x=c$ if $f\left(c\right)$ is the smallest function value when x is near c, whereas f has a local minimum at c if $f\left(c\right)$ is the smallest function value on the entire domain of f.
4) A function f has an absolute minimum at $x=c$ if $f\left(c\right)$ is the largest function value on the entire domain of f, whereas f has a local minimum at c if $f\left(c\right)$ is the largest function value when x is near c.
5) A function f has an absolute minimum at $x=c$ if $f\left(c\right)$ is the largest function value when x is near c, whereas f has a local minimum at c if $f\left(c\right)$ is the largest function value on the entire domain of f.

Nola Robson

Option 2 is correct:
A function f has an absolute minimum at $x=c$ if $f\left(c\right)$ is the smallest function value on the entire domain of f, whereas f has a local minimum at c if $f\left(c\right)$ is the smallest function value when x is near c.

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