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

Question

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

Nola Robson · Accepted Answer

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

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

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