Final answer:
To find the first derivative ′ and the original function . ″()=36, ′(0)=12, (0)=6, we need to integrate the given information.
Step-by-step explanation:
To find the first derivative ′ and the original function . ″()=36, ′(0)=12, (0)=6, we need to integrate the given information. Given that the second derivative ″() is equal to 36, we can find ′() by integrating ″() with respect to over time. This will give us the velocity function ′(). Consequently, we can find the original function () by integrating ′() with respect to over time. To find the constant of integration, we use the initial conditions, ′(0) = 12 and (0) = 6.