What does it indicate if the second derivative of a function is greater than zero?

When the second derivative of a function is greater than zero, it indicates that the function is concave upwards. This means that the slope of the function is increasing at that point, suggesting that if you were to draw a tangent line at that point, the function would lie above the tangent line in the immediate vicinity.

This concavity relationship is an important aspect of calculus because it helps to determine the behavior of the function's graph. When a function is concave upwards, any local minimum point would have a positive second derivative, reaffirming that the function curves upwards as you move away from that point, leading to an increase in function values.

Understanding concavity also plays a crucial role in identifying points of inflection, where the curvature changes, but having the second derivative greater than zero specifically confirms that a section of the function is indeed curving upward.