Mejiera said:Homework Statement
when you are finding the slope of a fuction at a point, you are finding the slope of that point with respect to what?
I don't understand how the square root function at point x = 4 slope is 1/4 shouldn't its slope be 1/2. please explain
Homework Equations
The Attempt at a Solution
Let f(x) = x1/2Mejiera said:Homework Statement
when you are finding the slope of a fuction at a point, you are finding the slope of that point with respect to what?
I don't understand how the square root function at point x = 4 slope is 1/4 shouldn't its slope be 1/2. please explain
Homework Equations
The Attempt at a Solution
More precisely, the 1/4 is the slope of the tangent line to the curve at a single point on the curve. It doesn't make sense to talk about the slope of a point.Mejiera said:Thank you Berkeman and Mark. I was making a silly mistake in assuming that a slope of a curve is costant throught the entire function. I researched on the difinition the derivative and it made me understand that 1/4 is not the slope of the entire curve, 1/4 is just the slope of a single point on the curve. Thanks again for the replies.
A derivative is a mathematical concept that represents the instantaneous rate of change of a function at a specific point. It measures how quickly the function is changing at that point.
To find the slope at a specific point on a graph, you can use the derivative formula: f'(x) = lim (h->0) (f(x+h) - f(x))/h. This will give you the slope of the tangent line at that point.
The slope at point x=4 represents the rate of change of the function at that specific point. It tells us how quickly the function is changing at x=4.
The slope at point x=4 is equal to the slope of the tangent line to the graph of the function at x=4. This tangent line touches the graph of the function at only one point and represents the instantaneous rate of change at that point.
Finding the slope at point x=4 allows us to understand the behavior of the function at that specific point. It can help us determine if the function is increasing or decreasing, and how rapidly it is changing at that point.