You are given the equation y=x^2. Determine whether or not the equation has any maximums or minimums and identify them (whether they are maximums or minimums).

The question has given us a function and wants us to determine whether or not any maximums/minimums exist (and if so identify then). We know maximums/minimums occur when the derivative of the equation is equal to zero. Hence we can different x^2 with respect to x, this gives us dy/dx=2x. As mentioned, the point occurs when dy/dx (the derivative) is zero. This gives us 2x=0, hence x=0, is going to be either a maximum or minimum.To determine which one it is, we must differentiate again. Differentiating 2x with respect to x gives us 2. As 2 is greater than 0, we know this is a minimum. (If it was negative, it would be a maximum, and if it equals zero it will be a stationary point of inflection.)