Chancellor Chopp has determined the number of hands she can

Chancellor Chopp has determined the number of hands she can shake in succession before collapsing by the function g(t) = 53 + 4.35t - 0.6t^2 + 0.05t^3 where t represents the number of months she has been DU. Compute g(6), g\'(6),and g\"(6). Give your answers with correct units. Use your computations in part (a) to complete the following sentences: After 6 months at DU, Chancellor Chopp can shake hands before collapsingand her \"handshake stamina\" (how many hands she can shake before she collapses) is at a rate of Moreover, the rate of change of her handshake stamina is at a rate of in that month. Determine the point of diminishing returns for Chancellor Chopp\'s handshake function. An appropriate sign chart is required for full credit. What is the maximum rate of change of the handshake function? Include units. (Note this is *not* the same as asking for the most possible hands she can shake).

Solution

g(t)=53+4.35t+0.6t²-0.05t³

Find first second derivative.

g\'(t) = 4.35 +1.2t -0.15 t²

g\"(t) = 1.2-0.3t

Substitute t =6 in g and the two derivatives to get

g(6) = 89.6

g\'(6) = 6.15

g\"(6) = 1.2-1.8 = -0.6

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g\'(t) = 0 gives

t = -2.708 or 10.708

As no of months cannot be negative

at t =10.708 g\'(t) =0

g\'(t)>0 , 0<t<10.708

g(10.708) = 106.4515

After 6 months he can shake 106.4515 - 89.6 = 16 number of hands before collapsing.

It was increasing before collapsing at the rate of g\'(10.708) = 0.00041

Maximum rate of handshake is at t = 4.