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Question
Find the absolute extrema of the following functions on the given closed interval.
f(x) = x2 – 12x + 10; [1, 2]
Solution
f(x) = x – 12x + 10
f'(x) = 2x – 12
f'(x) = 0
⇒ 2x – 12 = 0
x = 6 ∉ (1, 2)
Now, Evaluating f(x) at the end points x = 1, 2
f(1) = 1 – 12 + 10 = –1
f(2) = 4 – 24 + 10 = –10
Absolute maximum f(1) = –1
Absolute minimum f(2) = –10
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