Calc
posted by Amanda on .
f(x)=2ln(x^2+3)x Domain [3,5]
how do i find the absolute maximum value of this?

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.