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The question is missing parts. Here is the complete question.
Find the absolute maximum and absolute minimum values of f on the given interval.
, [ -2,8]
Answer: Absolute maximum: f(4) = 2.42;
Absolute minimum: f(-2) = -1.76;
Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.
<u>Absolute</u> <u>maximum</u> is a point where the function has its greatest possible value.
<u>Absolute</u> <u>minimum</u> is a point where the function has its least possible value.
The method for finding absolute extrema points is
1) Derivate the function;
2) Find the values of x that makes f'(x) = 0;
3) Using the interval boundary values and the x found above, determine the function value of each of those points;
4) The highest value is maximum, while the lowest value is minimum;
For the function given, absolute maximum and minimum points are:
Using the product rule, first derivative will be:
= 0
x = ±4
x can't be -4 because it is not in the interval [-2,8].
Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.
Therefore, absolute maximum is f(4) = 2.42 and
absolute minimum is f(-2) = -1.76