Derivative Question: Slope at Point x=4 Explained

[Mejiera]

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

 

[berkeman]

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

Slope is defined as rise/run, or delta_y/delta_x.

How do you mathematically find the slope of the function SQRT(x) at any given point? Show us the math of taking the derivative of SQRT(x) and plug in x=4. What answer do you get? (Please show your work)

 

[Mark44]

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) = x^1/2
Then f'(x) = (1/2)/x^1/2
f'(4) = ?

The slope is relative to the horizontal axis.

 

[Mejiera]

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.

 

[Mark44]

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.

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]

True