# Talk:Tangent Line to Convex Graph

Is the converse to this theorem true as well, that the tangent line being below the graph implies $f$ is concave up? If so, I can reword the theorem to make it a stronger statement. --GFauxPas 16:51, 27 November 2011 (CST)
A function (not necessarily continuous) is said to be concave up on an interval $I$ iff:
$\forall x,y,z\in I: x<y<z \implies f(y) > f(x) + \dfrac{y-x}{z-x}(f(z)-f(x))$
So I have to find a different terminology then. Larson defines a real differentiable function $f$ to be concave up on $\mathbb I$ iff $\forall x_1,x_2 \in \mathbb I, x_1 > x_2 \implies f'(x_1) > f'(x_2)$. He also doesn't use the term convex at all, just concave up and concave down. Khan Academy uses the same definition. Suggestions? --GFauxPas 13:36, 28 November 2011 (CST)
I can not give a name to the property and just say that $f'$ is strictly increasing on $\mathbb I$.? --GFauxPas 14:34, 28 November 2011 (CST)