Problem

a. Graph the function y1 = 5/x on the window [1, 10] by [0, 10]. By visual inspection, d...

a. Graph the function y1 = 5/x on the window [1, 10] by [0, 10]. By visual inspection, does the function have an absolute maximum value on this domain? An absolute minimum value?

b. Now change the x window to [0, 10] and answer the same questions. (We cannot now call [0, 10] the domain, since the function is not defined at 0.)

c. Based on the screen display, answer the same questions for the domain (0, ∞).

d. Is there a domain on which this function has an absolute maximum but no absolute minimum?

e. It was stated in the box on page 191 that a continuous function on a closed interval will always have absolute maximum and minimum values. Is this claim violated by the function f (x) = 5/x on [0, 10] [part (b)]? Is it violated by f (x) = 5/x on (0, ∞) [part (c)]?

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