find the volume of a water tank at time t=5
volume of water is v(t)= 4+2sin(t/6)
rate of change of volume of tank at t=5
+33616 To find volume at t = 5, simply substitute t by 5 in v(t) = 4 + 2sin(t/6)
v(5) = 4 + 2sin(5/6) or v(5) ≈ 5.48 (make sure the calculator is in radian mode when calculating sin(5/6))
To find rate of change of volume at t = 5, first differentiate v(t) with respect to t; v`(t) = (2t/6)cos(t/6), then replace t by 5:
v`(5) = (2*5/6)cos(5/6) or v`(5) ≈ 1.12
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