Replace the x in xy with 120- y so you have only one variable. Now, do you know how to "apply the derivative" to find where a function has a maximum or minimum?whitehorsey said:1. Find two numbers x and y whose sum is 120 and whose product is a maximum.
2. none
3. x + y = 120
xy = maximum
x = 120 - y
I wrote these down but I don't know what to do next. Can you please show me? :) Thank You!
The derivative measures the rate of change of a function at a specific point, which can be useful in various applications such as optimization, finding critical points, and understanding the behavior of a function.
The derivative of a function can be found by using the rules of differentiation, such as the power rule, product rule, chain rule, and quotient rule. These rules allow us to find the derivative of a function at any given point.
Yes, the derivative can be used to find the critical points of a function, where the derivative is equal to zero or undefined. These points can correspond to maximum or minimum values of the function.
The derivative of a function at a specific point is equal to the slope of the tangent line at that point. This means that the derivative can be used to find the slope of a tangent line to a curve at any given point.
Yes, there are many real-world applications of the derivative. For example, it can be used in economics to maximize profits, in physics to analyze motion and acceleration, and in biology to study growth and rates of change in populations.