# Slope of a function.

1. Aug 1, 2012

### Swetasuria

If there is an equation for a curve, its derivative will be the slope of the tangent.
Also, the derivative of a function is the limit of its slope.

What I understand from this is that (slope of tangent)=(limit of the same slope)

But this is wrong (right?). Please explain the mistake here.

2. Aug 1, 2012

### Dick

The derivative is the limit of the difference quotient. You can call this limit the slope. I have no idea what you mean by 'limit of the slope'.

3. Aug 1, 2012

### Swetasuria

Even so, I still can't understand the mistake I made.

4. Aug 1, 2012

### Muphrid

You're not taking the limit of the slope of tangent lines. You're taking the limit of the slope of secant lines. The secant line between points A and B has a slope that, in the limit that A and B come together, is the tangent line slope.

5. Aug 1, 2012

### Dick

What mistake? The limit of the derivative is not necessarily the derivative of the limit, which is the best way I can think of to make sense of your question. Take x^2*sin(1/x^2). It has a derivative at x=0. The limit of the derivative as x->0 doesn't exist.

6. Aug 2, 2012

### HallsofIvy

Staff Emeritus
Your mistake is talking about the "slope" of a function at all. "Slope" is only defined for lines. If a function is linear, then its graph is a straight line and so its graph (not the function) has a slope. If a function is not linear, then its graph is NOT a straight line and neither the graph nor the function has a "slope". We can, at each point, draw a line tangent to the graph and talk about its slope.