What am I doing wrong in finding the derivative and max/min?

[randy17]

1. The problem statement, all variables and given/known data

I need to find the max/min of y=(1)/(3+x^2)

2. Relevant equations

y=(1)/(3+x^2)

3. The attempt at a solution

I tried to find the derivative; y'= (3+x)^-2(1) = -2(3+x)^-3 = -2/(3+x)^3 or -2/3(3+x)^2?

Whats wrong with it?

 

[MarkFL]

We should expect that the given function will have a maximum where the denominator is a minimum, and this will be when \(\displaystyle x=0\).

If you wish to use the power/chain rules, then:

\(\displaystyle y(x)=(3+x^2)^{-1}\)

\(\displaystyle y'(x)=(-1)(3+x^2)^{-2}(2x)=-\dfrac{2x}{(3+x^2)^2}\)

The sign of the derivative will be the opposite of \(\displaystyle x\), hence the first derivative test tells us we have a maximum when \(\displaystyle x=0\).