The discussion clarifies the concept of finding the slope of the square root function, specifically at the point x=4. The slope is determined using the derivative of the function f(x) = x^(1/2), resulting in f'(x) = (1/2)x^(-1/2). When evaluated at x=4, the slope is calculated as f'(4) = 1/4. This indicates that the slope at this point is not constant across the curve, but rather represents the slope of the tangent line at that specific point.
PREREQUISITESStudents learning calculus, educators teaching derivative concepts, and anyone seeking to understand the behavior of functions at specific points.
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.