Let f be the function given by f(x)=sinxcosx/(x^2−4) on the closed interval [−2π,2π].

Question

On which of the following closed intervals is the function f guaranteed by the Extreme Value Theorem to have an absolute maximum and an absolute minimum?

A. [−2π,2π]

B. [−2,2]

C. [−1,1]

D. [π/2 , π]

Answer 1

Extreme Value Theorem requare: 1. Closed interval and 2. Continuos function. This function discontinuous at x = ±2. So closed in terval what dose not contain this points is [- 1, 1]. All other intervals contain or - 2. or 2 or both.

Answer: interval [- 1, 1]