This is my third question on my PSET

3. Please help your classmates, Naveed and Suzanne, who are quite confused about nding upper bounds. They are working on nding an upper bound for the function HI} = I30 + I2}005{1 2H on the interval {1, 3]. They reason as follows: I Naveed says: \"The biggest that 3:2 could be on the interval is at the righthand endpoint of the interval, where z = 3. So the biggest the function can be is H3] = |3(2 + 32) cos(3 _ 2}]|w(33)(l154l]3)m 17.33 . Just to be safe (and practical), I'm going to take 13 as my upper bound.\" - Suzanne says: \"But the biggest that the cos(.z' 2) can be on the interval is when rs = 2 (since that's where the input of the cosine is 0), so I think the biggest the function can be is 112) = i3(2 + 22) wsm 2m =(18)(1)= 18. So I think 18 is an upper bound too.\" To the right, you can see a plot of the function 3" x) 2 i3{2+:cg) cos(:c 2]] ls and it's clear that both Naveed and Suzanne are in trouble! [a] Referring to the plot, write two or three complete English sentences to explain to Naveed and Suzanne how they can see that they have both found an upper bound that is no good. Also explain what went wrong with their bounding process. [b] Referring to the plot, explain to Naveed and Suzanne what would be a reasonable upper bound to take, and how you know it's a good bound. {c} Naveed asks: \"How could we nd an upper bound without referring to the plot {for example, if we didn't have access to a. graphing calculator or WolframAlpha)?\" Find a good upper bound be practical! (If you're looking for examples of \"being practical\" see, for example, the solutions to the Numerical Methods and Error 1 worksheet.) {d} The bound you found in part (c) is probany not the same as the one you found in {b}. Explain to Suzanne and Naveed why this il't a