Explain the difference between an absolute minimum and a local minimum. 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. 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. 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) 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.