4. (5.1) The function f(t) = t(t 21)(t+ 1) can be used to model the measels pathogen esis curve in the gure below. Suppose symptoms develop on day 12. The area under the pathogenesis curve from t = 0 to t = 12 is equal to the total amount of infection needed to develop symptoms. Use six subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms. .\\.' l 15ml 2- x\" E r' E E ,5 -3 mm 7 .\\: .. f,\" .-' ' 2. l 2 l T; -. 5 '. _'-J l E inn ._ l 3: 'E 2 / / .. .) \\\\ FIGURE 17 _7_, 7 \\ ., .. . ., ' Measles paihagcncsls curve I] lEIH l2 ITIX 31 r . , Maul lama ,._ J. M. Hull; I l - \"YMMV [\"1\" . lnfccrinuanca'x' lnt'cctinus'nesx rrrfnyr Pathogen begun Symplmm ends Palhogen 35 [30024] IN 47. enters plasma appear Ls cleared (a) Divide the interval [0, 12] into six subintervals of equal width. What is the width of each subinterval? (b) Instead of using left or right endpoints as our sample points, we can use the midpoint of each subinterval. List the midpoints of the subintervals. (c) Using f(t) : t(t 21)(t + 1) to compute the heights of the rectangles, nd the estimated total amount of infection needed to develop symptoms. (d) If we had used left endpoints, would we have an over estimate, under estimate, or unclear? If we had used right endpoints, would we have an over estimate, under estimate, or unclear