Find the absolute maximum and minimum values of f, if

kloseyq

kloseyq

Answered question

2021-12-10

Find the absolute maximum and minimum values of f, if any, on the given interval, and state where those values occur.
f(x)=3x44x3,[0,1]

Answer & Explanation

Jordan Mitchell

Jordan Mitchell

Beginner2021-12-11Added 31 answers

Step 1
Given function is f(x)=3x44x3 and given interval is [0,1]
To find: The absolute maximum and minimum.
Solution:
Differentiating the given function with respect to x,
f(x)=ddx(3x44x3)
=12x312x2
Set first derivative equation equal to 0,
f'(x)=0
12x312x2=0
12x2(x1)=0
x2(x1)=0
x=0 or x=1
Step 2
So, critical points are 0 or 1.
Here, both critical points lies within given interval.
Also, critical points are endpoints of interval.
Now, we will find value of function at critical points and at endpoints of the interval.
f(0)=3(0)44(0)3
=0
f(1)=3(1)44(1)3
=3-4
=-1
Hence, absolute minimum value of given function is -1 and absolute maximum value is 0 .

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