Asked by Amanda
f(x)=2ln(x^2+3)-x Domain [-3,5]
how do i find the absolute maximum value of this?
how do i find the absolute maximum value of this?
Answers
Answered by
MathMate
To find the absolute maximum of a function within a finite domain, you can do:
find f'(x) and equate to zero to find the relative maxima and minima.
In this case, f'(x)=0 at x=1 and x=3.
By checking with f"(x) or otherwise, you will find that x=1 is a minimum, and x=3 is a maximum.
Evaluate f(3)=2ln(12)-3 = 1.97 approx.
Now evaluate function f(x) at limits of domain, namely f(-3)=2ln(12)+3=7.97 approx., and f(5)=2ln(28)-5=1.66 appro.
Thus the absolute maximum is at x=-3.
find f'(x) and equate to zero to find the relative maxima and minima.
In this case, f'(x)=0 at x=1 and x=3.
By checking with f"(x) or otherwise, you will find that x=1 is a minimum, and x=3 is a maximum.
Evaluate f(3)=2ln(12)-3 = 1.97 approx.
Now evaluate function f(x) at limits of domain, namely f(-3)=2ln(12)+3=7.97 approx., and f(5)=2ln(28)-5=1.66 appro.
Thus the absolute maximum is at x=-3.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.