e) determine the location and values of the absolute maximum and absolute minimum for the given function: f(x) = (- x + 2) ^ 4 where 0 <= x <= 3
Answers
Answer:
absolute minimum is 0 and absolute maximum is 16
Step-by-step explanation:
given that f(x)= (-x+2)⁴
-x+2 has whole power 4
the range is 0to infinity fo x belongs N
here 0<x>3
so maximum value is 16
SOLUTION
TO DETERMINE
The location and values of the absolute maximum and absolute minimum for the given function:
EVALUATION
Here the given function is
Now
Differentiating both sides with respect to x we get
Now for critical points we have
Now we find the value of f(x) at the critical point x = 2 and at the extremities of the given interval i.e 0 and 3
Thus we see that
∴ Absolute maximum value = 16 which occurs at x = 0
∴ Absolute minimum value = 0 which occurs at x = 2
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