Suppose that $\displaystyle I\subset \mathbb{R}$ is an open interval and that $\displaystyle f''(x) \geq 0$ for all $\displaystyle x\in I$. If $\displaystyle c \in I$ , show that the part of the graph of $\displaystyle f$ on $\displaystyle I$ is never below the tangent line to the graph at $\displaystyle (c,f(c))$ .