physicsguy98 said:Find f ' (2) given the following.
g(2) = 3 , g ' (2) = -2
h(2) = -1 , h ' (2) = 4
a. f(x) = 2g(x) + h(x)
b. f(x) = g(x) / h(x)
c. f(x) = 4 - h(x)
d. f(x) = g(x)*h(x)
A derivative is a mathematical concept that represents the rate of change of a function with respect to its input variables. It is a fundamental tool in calculus and is used to study the behavior of functions.
Derivatives are important because they allow us to analyze and understand the behavior of functions. They are used in many fields such as physics, engineering, economics, and statistics to model and solve various problems.
To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules allow you to find the derivative of a function by manipulating its terms and variables.
A derivative measures the instantaneous rate of change of a function, while an integral measures the accumulation of that function over a given interval. In other words, a derivative tells us how much a function is changing at a specific point, while an integral tells us the total value of that function over a certain range.
Derivatives have many practical applications in fields such as physics, engineering, economics, and finance. For example, derivatives can be used to model the motion of objects, optimize production processes, and calculate financial risk and pricing. They are also used in machine learning and data analysis to find patterns and make predictions.