Is Concave up an Underestimate?

If the tangent line between the point of tangency and the approximated point is below the curve (that is, the curve is concave up) the approximation is an underestimate (smaller) than the actual value; if above, then an overestimate.)

Is an underestimate concave up or down?

One of the important applications of the derivative at a point is to use it to approximate the value of a function at nearby points. ... Hence, the approximation is an underestimate. If the graph is concave down (second derivative is negative), the line will lie above the graph and the approximation is an overestimate.

How do you know if something is overestimate or underestimate?

The concavity will tell you whether your estimate is an underestimate or an overestimate. You can see this if you draw any concave up curve, then draw a tangent line somewhere to this curve and see if the line is above (overestimate) or below (underestimate); a concave down curve is similar.