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Question
Find the maximum and minimum value, if any, of the following function given by g(x) = − |x + 1| + 3.
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Solution
Given function g(x) = - |x + 1| + 3; g (3) ≤ 3∀ x ∈ R
Maximum value of -|x +1| = 0
Maximum value of g(x) = -|x + 1| + 3 = 0 + 3 = 3
occurs when x + 1 = 0, i.e., when x = -1.
Note that g(x) has no minimum value, for g (x) → a - ∞ as |x| ∞.
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