Understanding Math | Explaining the Meaning of y” > 0 and the Concept of Concave Upward Curves

When y” > 0, the curve is

When y” > 0, it means that the second derivative of the curve with respect to the x-axis is positive

When y” > 0, it means that the second derivative of the curve with respect to the x-axis is positive. This indicates that the curve is concave upward.

To understand this concept, let’s break it down step by step:

First, the first derivative of a function y'(x) represents the rate of change of the function. It tells us whether the function is increasing or decreasing at a particular point.

Next, the second derivative y”(x) represents the rate of change of the first derivative. In other words, it tells us how the slope of the function is changing with respect to x.

When y” > 0, it means that the slope of the curve is increasing as x increases. In terms of the shape of the curve, this implies that the curve is concave upward. In other words, if you were to draw a tangent line to the curve at any point, the curve would be curving upwards, forming a “U” shape.

To visualize this, imagine a smiley face emoji. The curved part of the smile, where the lips turn upward, resembles a curve that is concave upward. This is what a curve looks like when y” > 0.

In summary, when y” > 0, the curve is concave upward. This means that the slope of the curve is increasing as x increases, and the curve forms a “U” shape.

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