Pretty much as in the title, except one major condition: g(x_0) = m*x_0 + b. So, conditions are: g defined on the reals and is differentiable at x_0. g(x_0) = m*x_0 + b mx + b <= g(x) for all x Then show m = g'(x_0) I would love to use the intermediate value theorem, or extreme value theorem, or mean value theorem, but since we can only say g is differentiable at x_0 those can't apply since we don't have any intervals where those theorems would apply. Just wondering if there's an obvious theorem to apply here. Thanks!