Maximum and Minimum (CFU)

Front

What is a maximum in a function?

Back

A maximum is the highest point on the graph of a function, where the function value is greater than or equal to the values of the function at nearby points.

Front

What is a minimum in a function?

Back

A minimum is the lowest point on the graph of a function, where the function value is less than or equal to the values of the function at nearby points.

Front

How do you identify a maximum or minimum in a quadratic function?

Back

In a quadratic function of the form y = ax^2 + bx + c, if 'a' is negative, the vertex is a maximum; if 'a' is positive, the vertex is a minimum.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the function, depending on the direction the parabola opens.

Front

What is the significance of the coordinates (2, 0) in a function?

Back

The coordinates (2, 0) indicate a point on the graph of the function, which could represent a maximum, minimum, or another significant point.

Front

How can you determine if a function has a maximum or minimum?

Back

You can determine if a function has a maximum or minimum by analyzing its first derivative; if the derivative changes from positive to negative, there is a maximum, and if it changes from negative to positive, there is a minimum.

Front

What is the role of the first derivative in finding maxima and minima?

Back

The first derivative of a function indicates the slope of the function; critical points occur where the first derivative is zero or undefined, which can indicate potential maxima or minima.

Front

What is the second derivative test?

Back

The second derivative test helps determine the concavity of a function at critical points: if the second derivative is positive, the point is a minimum; if negative, it is a maximum.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing when its output values rise as the input values increase, and decreasing when its output values fall as the input values increase.

Front

What is the maximum value of a function?

Back

The maximum value of a function is the highest output value that the function can achieve over its domain.