The discussion revolves around understanding the concept of slope in relation to the derivative of the square root function, specifically at the point x = 4. Participants are examining the definition of slope and how it applies to a function at a specific point.
Some participants have acknowledged misconceptions regarding the constancy of slope across a curve and have begun to explore the specific nature of the slope at a single point. Guidance has been offered regarding the definition of the derivative and its implications for understanding slope.
There is an ongoing exploration of the definitions and assumptions related to slope and derivatives, with some participants reflecting on their previous misunderstandings. The discussion highlights the importance of distinguishing between the slope of a tangent line at a point versus the slope of the entire curve.
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 through 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.