You missed a set of parentheses.plugpoint said:Suppose [tex] f(x) = \frac{(x-3)^{4}}{x^{2}+2x} [/tex]. Find the derivative an determine the values for which it is equal to 0. So [tex] f'(x) = \frac{(x^{2}+2x)(4(x-3)^{3}) - (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} [/tex]. But now how would I go about finding the values for which the derivative equals 0? [tex] f'(x) = \frac{x^{2}+2x(4(x-3)^{3}) (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} = 0 [/tex]. Is it possible to factor?
Thanks
A derivative is a mathematical concept that measures the rate of change of a function at a specific point. It essentially tells us how much a function is changing at a particular point.
The derivative is an important tool in calculus and is used to solve a variety of problems in physics, engineering, economics, and other fields. It allows us to analyze the behavior of functions and make predictions based on their rates of change.
To find the derivative of a function, we use the rules of differentiation, which include the power rule, product rule, quotient rule, and chain rule. These rules help us to determine the rate of change of a function at a specific point.
The values of a derivative can vary depending on the function and the point at which it is evaluated. Generally, the value of a derivative represents the slope of a tangent line to the function at a specific point.
Derivatives can be used to solve a wide range of real-world problems, such as finding maximum and minimum values, optimizing functions, and predicting future behavior. They are particularly useful in physics and engineering for analyzing the motion of objects and in economics for understanding supply and demand relationships.