Step-by-step explanation:
g(t) = (412 - 6t + 9) dt
To find g'(t), we need to differentiate each term with respect to t separately:
g'(t) = d/dt (412) - d/dt (6t) + d/dt (9)
Since the derivative of a constant term is zero and the derivative of a constant multiplied by t is the constant itself, we have:
g'(t) = 0 - 6 + 0
Therefore, g'(t) = -6.
To find g'(3), substitute t = 3 into the derived expression:
g'(3) = -6
Hence, g'(3) = -6
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