Question 1112474
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If his temperature is really {{{98.6+4t/t^2+1}}}, then shortly after time 0 his temperature is hotter than the surface of the sun.<br>
So I assume you really mean his temperature is {{{98.6+4t/(t^2+1)}}}.  So<br>
{{{T(t) = 98.6+4t/(t^2+1)}}}
{{{dT/dt = ((t^2+1)(4)-(4t)(2t))/(t^2+1)^2 = (4-4t^2)/(t^2+1)^2}}}<br>
Answer a: {{{dT/dt = (4-4t^2)/(t^2+1)^2}}}<br>
Answer b: {{{T(2) = 98.6+4(2)/(2^2+1) = 98.6+8/5 = 98.6+1.6 = 100.2}}}<br>
Answer c: dT/dt at t=2 = {{{(4-4(2^2))/(2^2+1)^2 = (4-16)/(5^2) = -12/25}}}