1. Feb 28, 2012

We say that a slope can be calculated as the ratio of the perpendicular to the base , Then what does differentiation of the equation shows "dy/dx"?

2. Feb 28, 2012

### Number Nine

Re: Silly Math Question! Plzz help!

3. Feb 28, 2012

### Staff: Mentor

Re: Silly Math Question! Plzz help!

Differential calculus involves the evaluation of that Δy / Δx but taken to its extreme.

4. Feb 29, 2012

Re: Silly Math Question! Plzz help!

I just want to know what actually differentiation is apart from its equation ? what does it mean?

5. Feb 29, 2012

### Staff: Mentor

Re: Silly Math Question! Plzz help!

Differentiation is a way of calculating the slope at any point along a curve if you know that curve's equation.

6. Feb 29, 2012

Re: Silly Math Question! Plzz help!

Ya thats what i m saying suppose y =3x^2 then on differentiation i would get (dy/dx=6x) then at point x=3 the slope would be 18. Then isn't slope also calculated as (y2-y1)/(x2-x1) then at point x = 3 isn't it should be 9 ?

7. Feb 29, 2012

### Number Nine

Re: Silly Math Question! Plzz help!

No, because that equation gives you the slope of the line connecting two points; we don't have two points in this case, we only have one. Remember that when we construct the derivative we actually use the above slope formula to calculate the limit of the slope as the distance of two points approaches zero.

8. Mar 1, 2012

### Staff: Mentor

Re: Silly Math Question! Plzz help!

Yes. So if you take two points (x1,y1) and (x2,y2) on that curve, where x1 and x2 are very close to 3, then that quotient will be very close to 18.

9. Mar 1, 2012

Re: Silly Math Question! Plzz help!

Then what is the significance of one over the other ? I mean in which situation which one should i prefer ?

10. Mar 1, 2012

### Number Nine

Re: Silly Math Question! Plzz help!

This has already been explained to you. The slope formula gives you the slope of the line connecting two points; the derivative gives the slope of the tangent line at each point of the function.

11. Mar 1, 2012

### HallsofIvy

Re: Silly Math Question! Plzz help!

What appears to be puzzling you is the limit process. I recommend you go back and review "limits". It's probably in the chapter of your Calculus book just before the derivative is introduced!

12. Mar 1, 2012

### Staff: Mentor

Re: Silly Math Question! Plzz help!

Differentiation gives the exact value of the slope at any point you choose. Using the "pair of points" method gives an approximation, you are in effect approximating the curve with a straight line.

13. Mar 1, 2012