I am having trouble finding the critical points of this function, I was wondering if someone could help me out.
So I have a function $y = x\sqrt{4 - x^2}$. I know that I have to take the derivative then set that equal to 0 to find the critical points. \begin{align*} y &= x \sqrt{4 - x^2}\\ y' &= x \frac{d}{dx}\sqrt{4 - x^2} + \sqrt{4 - x^2}&& \text{(product rule)}\\ &= x\left(\frac{1}{2}(4 - x^2)^{-1/2}(-2x)\right) + \sqrt{4 - x^2} &&\text{(chain rule on square root)}\\ &= \frac{\frac{1}{2}x(-2x)}{(4-x^2)^{1/2}} + \sqrt{4-x^2}\\ &\qquad\qquad\text{(moved to denominator changed the exponent sign)} \end{align*}
This is where I am stuck, I cant seem to figure out how to proceed further, any help would be appreciated
Thanks