## anonymous 4 years ago find the absolute extrema of the following function on the given interval: f(x) = x^2 / (x^2 + 3) , [-1,1]

1. mathteacher1729

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

2. anonymous

yeah, we aren't allowed to use a calculator

3. anonymous

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

4. mathteacher1729

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

5. anonymous

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

6. anonymous

oh okay. thank you