Question

find the absolute extrema of the following function on the given interval:
f(x) = x^2 / (x^2 + 3) , [-1,1]

Answer 1

I guess you have to use calculus and are not allowed to use a calculator?

Answer 2

yeah, we aren't allowed to use a calculator

Answer 3

\[
f'(x)=\frac{6
x}{\left(x^2+3\right)^2}\\
f'(x) >0 \text { if} x >0\\
f'(x) <0 \text { if} x<0\\
f'(x) =0 \text { if} x=0\\
\]

Answer 4

Do you know how to use the 1st derivative test?

Answer 5

Hence we have to examine
f(1)=1/4
f(-1)=1/4
f(0)=0

Max 1/4 and Min=0

Answer 6

oh okay. thank you