stonecoldgen said:it's just something thechnical
let's say i have the function x2+3x+2
when they say f(x+[itex]\Delta[/itex]x)
is it (x+[itex]\Delta[/itex]x)2+2(x+[itex]\Delta[/itex]x)+2
or
another way?
Dick said:It's that. Except you have 3 in the first expression and a 2 in the second in the linear term. Typo, I guess?
A derivative is a mathematical concept that represents the rate at which one quantity changes in relation to another quantity. In simpler terms, it measures the slope or rate of change of a function at a specific point.
The derivative of a function is calculated by using the limit concept, specifically the limit of the difference quotient. This involves finding the slope of a line tangent to the function at a specific point, which is also known as the instantaneous rate of change.
Derivatives are important because they have numerous applications in various fields such as physics, economics, engineering, and more. They are used to model real-world phenomena and make predictions about the behavior of a system.
A derivative represents the rate of change of a function, while an antiderivative represents the original function before differentiation. In other words, a derivative is the opposite of an antiderivative and they are calculated using inverse operations.
Yes, derivatives can be negative. The sign of a derivative indicates the direction of change of a function. A negative derivative means that the function is decreasing, while a positive derivative means that the function is increasing.