Mastering The Math Behind Minimum Points: Finding And The Lowest Point On A Curve

minimum point

the point where the graph changes from decreasing to increasing

The minimum point is a point on a graph where the curve changes direction from downward to upward. In other words, it is the lowest point on a curve.

Mathematically, the minimum point of a curve can be found by taking the derivative of the function and setting it equal to zero. We then solve for the corresponding values of x and y to obtain the coordinates of the minimum point.

When graphing a quadratic function, the minimum point is also known as the vertex. The vertex is obtained by using the formula:

x = -b/2a

y = f(x)

where a, b and c are the coefficients of the quadratic function f(x). This formula gives the x-coordinate of the vertex, which is the same as the value of x at the minimum point. Substituting this value into the original equation gives the corresponding y-value at the minimum point.

It is important to note that not all functions have a minimum point. Some functions may have a maximum point or may not have any extreme points at all. Furthermore, the concept of a minimum point can also be extended to more complex functions with multiple variables, where the minimum point represents the optimal solution to a problem.

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