$2.$ Show that if a function is continuously differentiable, it is strictly convex if and only if a linear approximation to the function always underestimates it$.($Hint: Show that if condition $[2\mathrm{.}4$a$]$ holds, then $[2\mathrm{.}4$b$]$ is true, and if $[2\mathrm{.}4$b$]$ holds, then $[2\mathrm{.}4$a$]$ is true.$)$