(a) Sketch the graph of a function on [-1,2] that has an absolute maximum but no local maximum.
(b) Sketch the graph of a function on [-1,2] and it satisfies the conditions that the graph has local maximum but no absolute maximum.
(a) The graph is sketched.
(b) The graph is sketched.
The given function that has an absolute maximum but no local maximum.
Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.
The graph of the given function is:
Let be represented in the x-axis and the value of the function f (x) be represented in the y-axis. Local maximum is the point in the considered interval [-1,2] of the domain at which the function attains its maximum value. Consider any greatest point on the interval but should not consider the end points as the local maximum does not at end points. Hence, consider the point [1,1] . Absolute maximum is any point of the domain at which the function attains its [-1,2] maximum value. Draw the graph of the function in such a way that it satisfies the given conditions as shown below in Figure:
From Figure, it is observed that the graph has local maximum at x = 1 . Since the curve has hole at x = -1 , the point is not included in the domain. Therefore, it has no absolute maximum at x = -1 .
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