Question

maximum and minimum point of y=x²+1/x​

Answer 1

Answer:

When you want to find out the extremum points (min-max) of a function, you first take its second derivative and analyze its behaviour in a given interval.

y”=(x^2)”=2 -> this positive result implies that y variable is always increasing in the region x=-+infinity. We can conclude that there can only be 1 extremum point and its a minimum.

We then need to take its first derivative and equate it to zero to find out the x value that makes this function minimum.

y’=(x^2)’=0 -> x=0

Therefore, we say that y function has its minimum value at x=0.

Since: y(x=0)=0^2=0 -> The solution is y=0.

Hope this helps.