Use implicit differentiation.claytonh4 said:Homework Statement
Find the instantaneous rate of change for the function y2+(xy+1)3=0 at (2,-1)
Homework Equations
N/A
The Attempt at a Solution
I tried getting it into a "y=" format but I don't really understand how to deal with the y when it's squared in one part and cubed in the other. This is as far as I could figure:
y=(-(xy+1)3)1/2
Thanks for any help!
The Instantaneous Rate of Change Problem is a mathematical concept that involves finding the rate of change of a function at a specific point. It is used to calculate the slope of a curve at a particular point, also known as the derivative.
Average rate of change is the overall change in a function over a given interval, while instantaneous rate of change is the rate of change at a specific point within that interval. Average rate of change is calculated by dividing the change in output by the change in input, while instantaneous rate of change is calculated using the limit of the average rate of change as the interval approaches zero.
The instantaneous rate of change is represented by the derivative of a function. It is written as f'(x), where f is the original function and x is the point at which the rate of change is being calculated.
In physics, velocity is defined as the instantaneous rate of change of displacement with respect to time. In other words, velocity is the derivative of displacement. This means that the instantaneous rate of change and velocity are closely related concepts.
The instantaneous rate of change has many real-world applications, such as in physics, economics, and engineering. For example, it is used to calculate the acceleration of an object, the rate of change of stock prices, and the rate of change of temperature in a chemical reaction. It is also used in optimization problems to find the maximum or minimum values of a function.