To calculate: The absolute maximum value of curve,
The maximum value with six decimal is .
The curve is given as:
We seek a solution of , starting from an initial estimate .
For , compute the next approximation by
and so on.
Absolute Maximum Value: The critical numbers of function f within the interval . Substitute the values in function and the largest value obtained by critical number is the absolute maximum value.
Consider the curve ,
(by product rule)
Hence, we get the critical numbers from . In other words is used to find out roots using Newton’s Method.
Now, let initial approximation be
The second approximation is .
The third approximation is .
The function values at critical numbers and endpoints are:-
So, at end intervals
At critical point
Therefore, the absolute maximum value of curve is .
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