Looking Ahead to Calculus A key theorem in calculus, the
Chapter 1, Problem 1.172(choose chapter or problem)
Looking Ahead to Calculus A key theorem in calculus, the Extreme Value Theorem, states, if a function f is continuous on a closed interval [a, b] then has both a maximum value and a minimum value on the interval. For each of the following functions, verify that the function is continuous on the given interval and find the maximum and minimum values of the function and the x values at which these extrema occur.
(a) \(f(x)=x^{2}-3,[-2,4]\)
(b) \(f(x)=\frac{1}{x},[1,5]\)
(c) \(f(x)=|x+1|+2,[-4,1]\)
(d) \(f(x)=\sqrt{x^{2}+9},[-4,4]\)
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