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
ANSWERED
asked 2021-06-12
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.

Answers (1)

2021-06-13
Step 1
Option b is correct:
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.
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