Explain the difference between an absolute minimum and a local minimum. There is

Question

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

Explanation / Answer

The absolute max and min (also called the global max and min) are the smallest and largest values of f(x) over the entire domain, while the local max and min are the smallest and largest values of f(x) near x.

that's why b option is correct, which says---->(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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