Consider the function f(x)=xe^{-5x}, 0\le x\le 2. This function has an

jamessinatraaa

jamessinatraaa

Answered question

2021-12-10

Consider the function f(x)=xe5x,0x2.
This function has an absolute minimum value equal to: B
which is attained at x=B
and an absolute maximum value equal to: B
which is attained at x=B

Answer & Explanation

redhotdevil13l3

redhotdevil13l3

Beginner2021-12-11Added 30 answers

Step 1
Given function is, 
f(x)=xe5x,0x2
Find the critical points.
f(x)=(xe5x)
=x(5e5x)+e5x(1)
=5xe5x+e5x
=e5x(15x)
Step 2
Calculate the value of x by equating the derivative to 0.

f'(x)=0
e5x(15x)=0
e5x0,15x=0x=15
Step 3
Since the given integral is [0, 2], check for x = 0, 1/5 and 2.
f(0)=(0)e5(0)=0
f(15)=(15)e5(15)=(15)e1=15e
f(2)=(2)e5(2)=2e10
Therefore, the absolute maximum value of 15e attained at x=15.
Absolute minimum value of 0 attained at x=0.

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