# Calc

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f(x)=2ln(x^2+3)-x Domain [-3,5]

how do i find the absolute maximum value of this?

• Calc -

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.

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