Discovering The Minimum Value Of A Function: Methods For Quadratic, Linear, And More

Minimum value

The y-value of the lowest point on the graph of the function.

The minimum value of a function is the lowest output or y-value that the function can produce across its entire domain. In other words, it is the smallest value that the function can attain. We can find the minimum value of a function by different methods depending on the type of function:

1. For a quadratic function, where the variable is squared or raised to the power of 2, we can use the formula -b/2a to find the x-coordinate of the vertex of the parabola. Once we have the x-coordinate, we can substitute it into the function to find the associated y-coordinate, which will be the minimum value of the function.

2. For a linear function, where the variable is raised to the power of 1, we can use calculus by finding the derivative of the function and setting it equal to zero. Once we find the critical point, we can then determine whether it is a minimum or maximum by looking at the sign of the second derivative.

3. For other types of functions, we may need to use calculus to find the minimum value. We can find the derivative of the function, set it equal to zero to find the critical points, and then use the second derivative test to determine whether the critical points are local or global minima.

It’s important to note that there may not always be a minimum value for a function. Functions that are unbounded below, or have asymptotes that approach negative infinity, do not have a minimum value.

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