Find the absolute extrema on the given interval. f(x)=x-\sqrt[3]{x}, [-1,4]

nuais6lfp 2021-12-03 Answered
Find the absolute extrema on the given interval.
f(x)=x3{x},[1,4]
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Expert Answer

oces3y
Answered 2021-12-04 Author has 21 answers
Given function is f(x)=x3{x} and interval is [-1,4].
We need to find critical points of the function.
Differentiating the given function with respect to x,
f(x)=ddx(x3{x})
=ddx(x)ddx(x13)
=113x131
=113x23
Putting first derivative equals to zero.
113x23=0
13x23=1
x23=3
x=332
x=1332
x=133
Therefore, critical value of the function is 133.
Step 5
133 lies in the interval [-1,4].
Now we will evaluate the function at the endpoints of the interval and critical value.
f(1)=13{1}
=1-1
=0
f(133)=13{(33)}
=13{5.19}
=1-2.27=-1.27
Step 6
f(4)=43{4}
=4-1.58
=2.42
The absolute maximum value of the function is 2.42 at x=4.
The absolute minimum value of the function is -1.27 at x=133.
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