calculus
posted by Roger .
Suppose the function G(t) represents a test grade (out of 100 points) as a function of hours studied. If
G(t)=0.046t^3+0.915t^2+38.005 points, what is (dG/dt)when t=4? Round your answer to the nearest point per hour.
a. 50 points per hour
b. 3 points per hour
c. 5 points per hour
d. 7 points per hour
e. 20 points per hour

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Derivative of t ^ 3 = 3 * t ^ 2
Derivative of t ^ 2 = 2 * t
Derivative of 38.005 = 0
dG / dt =  0.046 * 3 * t ^ 2 + 0.915 * 2 t + 0 =  0.138 * t ^ 2 + 1.83 * t
When t = 4
then :
dG / dt =  0.138 * 4 ^ 2 + 1.83 * 4
dG / dt =  0.138 * 16 + 7 . 32
dG / dt =  2.208 + 7.32
dG / dt = 5.112
Rounded to the nearest point per hour :
dG / dt = 5 points per hour