Projectile motion of the ball is given with the function s(t) = 4.9t² + 15t + 11, where t is time and s is the position of the object in motion.

a. Write a code in Python to plot the function, s(t) = 4.9t² + 15t + 11, from t = 1 to 4. (Hint: You need to import matplotlib.pyplot and numpy libraries).

b. Using calculus, determine the time t at which the ball reaches its highest point. Verify your answer by referring to the graph.(Hint: Function goes through an extreme value (i.e: minimum or maximum ) at the point where the first derivative of the function is zero).