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Given the functions 
and 
, 
.
Let a = 4. Calculate the zeros and the turning points of the functions f and g and draw their graphs in the same coordinate system.
Prove that the graphs of the functions f and g intersect at right angles at the point 
for every .
Prove that the area of the bounded by the graphs of the functions on the interval 
is equal to 
.
At what value of a is the area between the graphs of functions f and g minimal?
