AP Calculus ABeasymcq1 pt
Which of the following functions is guaranteed to have both a maximum and minimum value on the closed interval [0, 2π]?
A.B) f(x) = 1/x
B.A) f(x) = tan(x)
C.D) f(x) = ln(x)
D.C) f(x) = sin(x)
Explanation
Core Concept
The Extreme Value Theorem states that if a function is continuous on a closed interval, then it must have both a maximum and minimum value on that interval. Among the options, sin(x) is the only function that is continuous on the closed interval [0, 2π]. The other functions either have discontinuities in this interval or are undefined at some points.
Correct Answer
DC) f(x) = sin(x)
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