Find the absolute maximum value and the absolute minimum value

regatamin2

regatamin2

Answered question

2021-12-13

Find the absolute maximum value and the absolute minimum value of the following function
f(x)=2|x| on [-1,6]

Answer & Explanation

otoplilp1

otoplilp1

Beginner2021-12-14Added 41 answers

Step 1 Given
f(x)=2|x|
f'(x)=2, if x>0
=-2 if x<0
Step 2 Finding the absolute maximum value and the absolute minimum value
When x[0,6], f(x) is increasing
When x[1.0], f(x) is decreasing
f(-1)=2(-1)
=2
f(0)=0
f(6)=12
f(x) is minimum at x=0, and absolute minimum value =f(0)=2(0)=0
f(x) is maximum at x=6 and absolute maximum value = 12

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