MATH 112 Your car has no cup holder, so you must place your filled coffee cup on the passenger seat beside you when you start out in the morning

<strong>MATH</strong> <strong>112</strong> <strong>Your</strong> <strong>car</strong> <strong>has</strong> <strong>no</strong> <strong>cup</strong>
<strong>holder</strong>, <strong>so</strong> <strong>you</strong> <strong>must</strong> <strong>place</strong> <strong>you</strong>r <strong>filled</strong>
<strong>coffee</strong> <strong>cup</strong> on the passenger seat
beside <strong>you</strong> when <strong>you</strong> start out in the
morning
BUY HERE⬊
https://www.homeworkmade.com/math
-<strong>112</strong>-<strong>you</strong>r-<strong>car</strong>-<strong>has</strong>-<strong>no</strong>-<strong>cup</strong>-<strong>holder</strong>-<strong>so</strong><strong>you</strong>-<strong>must</strong>-<strong>place</strong>-<strong>you</strong>r-<strong>filled</strong>-<strong>coffee</strong>-<strong>cup</strong>on-the-passenger-seat-beside-<strong>you</strong>when-<strong>you</strong>-start-out-in-the-morning/
<strong>Your</strong> <strong>car</strong> <strong>has</strong> <strong>no</strong> <strong>cup</strong> <strong>holder</strong>, <strong>so</strong> <strong>you</strong> <strong>must</strong> <strong>place</strong> <strong>you</strong>r <strong>filled</strong> <strong>coffee</strong> <strong>cup</strong> on the passenger seat beside <strong>you</strong> when
<strong>you</strong> start out in the morning. Bitter experience <strong>has</strong> taught <strong>you</strong> that the <strong>cup</strong> is least stable – and most prone to
spill – when it is completely full, but becomes more stable as <strong>you</strong> drink the <strong>coffee</strong> and thereby lower its level in
the <strong>cup</strong>.
The picture on the left shows a <strong>coffee</strong> <strong>cup</strong> partially <strong>filled</strong> with <strong>coffee</strong>. We will assume that it is the most stable
when the centroid of the <strong>cup</strong>-plus-<strong>coffee</strong> is lowest.
Assume that the centroid of the <strong>cup</strong>-plus-<strong>coffee</strong> is represented by the function of the depth y
(in cm) of the <strong>coffee</strong> in the <strong>cup</strong>:
where
Calculate the optimal depth y of the <strong>coffee</strong> in <strong>you</strong>r <strong>cup</strong>. (HINT: the centroid function is lowest when
f ′ (y) = 0.) Round <strong>you</strong>r answer to the nearest whole number. Include the sketch of the centroid function f(y) and
verify <strong>you</strong>r <strong>so</strong>lution graphically.