I was reading the Considere's criteria:for necking. The link: http://www.steeluniversity.org/content/html/eng/1230-0120-pu.htm [Broken] describes the math and the phenomenon involved (i.e mainly necking begins when the increase load bearing capacity is balanced due to reduction in cross section area). The final equation in the above link gived: d_sigma_t / d_epsilon_t = sigma_t. Can we state the above equation as follows; 1) Necking begins when the slope of the true stress vs true strain curve is equal to the ultimate tensile stress? OR AS WELL 2) At the ultimate tensile stress, the slope of the ultimate tensile stress to the corresponding strain (i.e drawing a tangent at that point) is equal to the ultimate tensile stress itself. Are these both correct?