Thread: Local Extrema

Started doing local extrema which concepts I understand. I am struggling with two problems which I was hoping to get some help on. The problem states to find the critical points and local min and max. I know to take first and second derivative to find the values but thats where i am messing up. Thanks for the help.

9) h(y)= y^{2 -} 1/y

15) f(x)= pi - (x-2)^​2/3

9) h(y)= y² - 1/y

Remember 1/y= y^-1
The derivative of 1/y is therefore -1y^-2
The derivative of y² is 2y
You can then solve 2y - (-1y^-2)= 0 for y

15) f(x)= pi - (x-2)​2/3
Since pi is a constant the derivative of pi is 0
The derivative of (x-2)^2/3 is (2/3)(x-2)^-1/3
So you can solve -(2/3)(x-2)^-1/3= 0 for x