The first and second derivitave tests are part of the broader topic of curve sketching. Eventually, we will be able to sketch a graph using this knowledge. The first derivitave test is to determine increasing or decreasing behavior on a graph. If the first derivative of the function goes from positive to negative then there is a local maximum at that point and if it changes from neg to positive, then there is a local minimum. There is no local max or min if the derivative does not change sign. The... read more
