Let {{MATH_236}}, for {{MATH_237}}. Locate the global extremums of {{MATH_238}} on the closed interval {{MATH_239}}. Does the function {{MATH_240}} satisfy the conditions of the Extreme Value Theorem on its domain? {{CMD_241}} {{CMD_242}}Yes, because {{MATH_243}} is continuous on {{MATH_244}}.{{CMD_245}} {{CMD_246}}Yes, because {{MATH_247}} is continuous on {{MATH_248}}.{{CMD_249}} {{CMD_250}}No, because {{MATH_251}} is not continuous on {{MATH_252}}.{{CMD_253}} {{CMD_254}}No, because {{MATH_255}} is not differentiable on {{MATH_256}}.{{CMD_257}} {{CMD_258}} Therefore, the Extreme Value Theorem guarantees that the function {{MATH_259}} attains both global extremums on its domain. The global extremums occur at the end points or at critical points. Find the critical points of {{MATH_260}}. First, compute the derivative of {{MATH_261}}. {{CMD_262}} {{MATH_263}} {{CMD_264}} In order to find the critical points of {{MATH_265}}, we have to solve the equation {{CMD_266}} {{MATH_267}} {{CMD_268}} It follows that the function {{MATH_269}} has only one critical point {{MATH_270}}. Find {{MATH_271}}. {{CMD_272}} {{MATH_273}} {{CMD_274}} In order to locate the global extremums of {{MATH_275}}, we have to evaluate {{MATH_276}} at the end points and at the critical point. {{CMD_277}} {{MATH_278}} {{CMD_279}} {{CMD_280}} {{MATH_281}} {{CMD_282}} {{CMD_283}} {{MATH_284}} {{CMD_285}} Order the three values, {{MATH_286}}, {{MATH_287}}, and {{MATH_288}}, from smallest to largest. You should replace {{MATH_289}} with its value, when you write {{MATH_290}} in your answer below. {{CMD_291}} {{MATH_292}} {{CMD_293}} Based on this comparison, find the location of the global minimum and global maximum of {{MATH_294}}. Circle the correct answer. {{CMD_295}} {{CMD_296}}{{MATH_297}} has a global maximum at {{MATH_298}} and global minimum at {{MATH_299}}.{{CMD_300}} {{CMD_301}}{{MATH_302}} has a global maximum at {{MATH_303}} and global minimum at {{MATH_304}}.{{CMD_305}} {{CMD_306}} {{MATH_307}} has a global maximum at {{MATH_308}} and global minimum at {{MATH_309}}.{{CMD_310}} {{CMD_311}}{{MATH_312}} has a global maximum at {{MATH_313}} and global minimum at {{MATH_314}}.{{CMD_315}} {{CMD_316}}{{MATH_317}} has a global maximum at {{MATH_318}} and global minimum at {{MATH_319}}.{{CMD_320}} {{CMD_321}}{{MATH_322}} has a global maximum at {{MATH_323}} and global minimum at {{MATH_324}}.{{CMD_325}} {{CMD_326}} {{CMD_327}}