Question

# Explain the difference between an absolute minimum and a local minimum. a) There is no difference. b) A function f has an absolute minimum at x=c if f

Analyzing functions
Explain the difference between an absolute minimum and a local minimum.
a) There is no difference.
b) A function f has an absolute minimum at $$x=c$$ if $$f(c)$$ is the smallest function value on the entire domain.
c) A function f has an absolute minimum at $$x=c$$ if $$f(c)$$ is the smallest function value when x is near c, whereas f has a local minimum at c if $$f(c)$$ is the smallest function value on the entire domain of f.
d) A function f has an absolute minimum at $$x=c$$ if $$f(c)$$ is the largest function value on the entire domain of f, whereas f has a local minimum at c if $$f(c)$$ is the largest function value when x is near c.
e) A function f has an absolute minimum at $$x=c$$ if $$f(c)$$ is the largest function value when x is near c, whereas f has a local minimum at c if $$f(c)$$ is the largest function value on the entire domain of f.

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