The height (in feet) of a rocket t seconds into flight is given by s = -t^3 + 96t^2 + 195t + 5. a) Find the maximum height attained by the rocket. b) Find the maximum velocity attained by the rocket.
Added by Eric O.
Step 1
To find the velocity of the rocket, differentiate the height function \( s(t) = -t^3 + 96t^2 + 195t + 5 \) with respect to time \( t \). The derivative \( s'(t) \) represents the velocity function \( v(t) \). \[ v(t) = s'(t) = -3t^2 + 192t + 195. \] Show more…
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