Suppose the position of an object moving horizontally after t seconds is given by the following function s=​f(t), where s is measured in​ feet, with s>0 corresponding to positions right of the origin. ​f(t)=t3−12t^2+45t​; 0≤t≤7 a. Graph the position function. b. Find and graph the velocity function. When is the object​ stationary, moving to the​ right, and moving to the​ left? c. Determine the velocity and acceleration of the object at t=1. d. Determine the acceleration of the object when its velocity is zero. e. On what intervals is the speed​ increasing?

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