If and
, then you can replace
in either equation with the equivalent expression given by the other equation. In this case, you have
and you can solve for .
Then .
For the second system, you can write
Then substitute this into the second equation and you get
so that
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
