To Identify: The curves and on given graph and give proper explanation.
In the given graph,, , and .
The given graph is shown as in Figure 1,
Observe the graph of c and d carefully.
The point where is the same point where graph of has horizontal tangent.
Recall that the derivative of a function is zero where the function has a horizontal tangent.
is the derivative of the graph .
Thus, . (1)
Observe the graph of b and c carefully.
The slope of c has negative value when . Only the curve b has negative value when . Also, it is observed that the slope of c has positive value when while the curve b has positive value when .
Thus, . (2)
Observe the graph of b and a carefully.
The slope of b has positive value when . Only the curve a has positive value when .
Thus, . (3)
From (1), (2) and (3), it is concluded that, , and
Thus, , , and .
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