Find the absolute maximum and absolute minimum values of function on the given interval. f(x)=5+54x-2x^3, [0,4]

usagirl007A 2021-03-06 Answered
Find the absolute maximum and absolute minimum values of function on the given interval.
f(x)=5+54x2x3,[0,4]
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Expert Answer

tabuordg
Answered 2021-03-07 Author has 99 answers

Step 1
Given:
Given that function f(x)=5+54x2x3
The given interval is [0,4]
To find:
we have to find the absolute maximum and absolute minimum
Step 2
Here f(x)=5+54x2x3 ...(1) and the interval is [0,4]
Differentiate (1) w.r.t.x, we get
ddxf(x)=ddx(5+54x2x3)
f(x)=546x2
set f(x)=0
546x2=0
6x2=54
x2=9
x=3 and x=3
but x=3[0,4]
and it also contain the critical point x=0
Step 3
Hence, the critical points is x=3 and x=0
Now, f(x)=5+54x2x3
For x=3
f(3)=5+54(3)2(3)3=5+16254
=113
Thus, the absolute value is maximum at x=3
Now, f(x)=5+54x2x3
For x=0
f(0)=5
Thus, the absolute value is minimum at x=0

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