Whether the statement, if f is continuous on (a,b) then f attains an absolute maximum value and an absolute minimum value at some numbers c and d in (a,b) is true or false.
The given statement is false.
If the graph of the function is a line parallel to x-axis, then there will be no absolute minimum or an absolute maximum.
If the graph of the function is a line which is defined on any open interval (a, b), then there will be no absolute minimum or an absolute maximum.
From Figure 1, it can be identified that either the horizontal line or a straight line does not attain its absolute minimum or absolute maximum.
Therefore, the given statement is false.
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