Find the absolute maximum and absolute minimum values of f

Reginald Metcalf

Reginald Metcalf

Answered question

2021-12-11

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=x2ln(x),[12,7]
absolute minimum value
absolute maximum value

Answer & Explanation

usaho4w

usaho4w

Beginner2021-12-12Added 39 answers

Step 1
f(x)=x2ln(x)
f(x)=2x3ln(x)+x2x
f(x)=2ln(x)x3+1x3
f'(x)=0
2ln(x)x3+1x3=0
1x3=2ln(x)x3
ln(x)=12
x=e12
x=1.65
Step 2
f(0.5)=0.52ln(0.5)=2.77
f(1.65)=1.652ln(1.65)=0.184
f(7)=72ln(7)=0.04
Absolute minimum at x = 0.5 , value = -2.77
Absolute maximum at x = 1.65, value = 0.184

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?