The maximum value of a function is the largest y-value of that function.
- true ***
- false
yes, true if y = f(x) for example
true
The maximum value of a function is indeed the largest y-value of that function. It corresponds to the highest point on the graph of the function. To find the maximum value of a function, you can use various techniques depending on the nature of the function.
For example, if you have a quadratic function in the form f(x) = ax^2 + bx + c, where a, b, and c are constants, the maximum value occurs at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and then you can simply substitute this value into the function to find the corresponding y-coordinate.
Similarly, if you have a continuous function on a closed interval, you can use the Extreme Value Theorem to determine the maximum value. According to this theorem, if a function is continuous on a closed interval [a, b], then the function must attain its maximum and minimum values at either the endpoints or at critical points (points where the derivative is zero or undefined) within the interval. To find the maximum value, you can evaluate the function at these critical points and the endpoints, and then choose the largest y-value.
In some cases, finding the maximum value may require more advanced techniques like optimization algorithms or calculus concepts such as derivatives and critical points. However, the basic idea remains the same - the maximum value corresponds to the highest y-value of the function.