# Slope of tangent

1. Dec 7, 2011

### Willowz

1. The problem statement, all variables and given/known data
show that the tangent line to the curve y=x^3 at any point (a,a^3) meets the curve again at a point where the slope is four times the slop at (a,a^3).

2. Relevant equations
y=3x^2, point slope formula

3. The attempt at a solution
Not really sure where to begin. A hint should be enough.

2. Dec 7, 2011

### micromass

Staff Emeritus
Can you find the equation of the tangent line at a?

3. Dec 7, 2011

### Willowz

That would be, y=3a^2?

4. Dec 7, 2011

### micromass

Staff Emeritus
No, where in earth did you get that?? A tangent line is a line. Its equation must contain an x and a y variable.

5. Dec 7, 2011

### Willowz

Not sure what you are asking for. Could you clarify?

6. Dec 7, 2011

### micromass

Staff Emeritus
I'm asking for the equation of the tangent line at the curve. How do you find the tangent line at a curve?? What is the slope of such a tangent line??

7. Dec 7, 2011

### HallsofIvy

Staff Emeritus
Do you know what the equation of a line, perhaps with slope m and passing through point $(x_0, y_0)$ looks like?

8. Dec 7, 2011

### Willowz

I got y=3a^2*x -2a^3 for the tangent line. Is that alright?

9. Dec 7, 2011

### chrisbaird

The equation of a line is y = m x + b. You need to find the right slope m and intercept b that will make the line be the right one that is tangent and touches a certain point.

10. Dec 7, 2011

### Willowz

Yes, I do have an idea how it may look like. A straight line touching the curve and then intersecting the function at some other point where the slope is four times the value of the tangent line.

11. Dec 7, 2011

### HallsofIvy

Staff Emeritus
The scary thing is that you think that answers my question. I asked about what the equation looks like and you said nothing about an equation.

12. Dec 7, 2011