I'm working through a partial differentiation problem, to which I have the answer. The function being 4x^2+4xy-y^3-2x+2 to which the stationary points must be obtained and classified. At the end of the working out, when partial differentiation is conducted and a number of -32 is obtained, it states that because this is a negative number this is a "saddle point". Is this another term for a "point of inflection"? How can they make this claim? I thought since the number obtained is negative it would therefore be a maximum turning point. The second number obtained with the second partial differentiation is 32, and it states since this is a positive number this is a minimum turning point; which I understand. Thank you.