# Question on the slope of the tangent

1. Mar 5, 2007

### kiss89

Find the points on the graph of y= (1/3)x^3-5x- (4/x) at which the slope of the tangent is horizontal.

what i know:
- we have to use m=[f(a+h)-f(a)]/h
- if we change the equation we can get 3x^4 - 15x^2 -12
- the slope of the tangent is zero.

THANX

2. Mar 6, 2007

### Staff: Mentor

hint: how does the derivative of a function relate to the slope of the tangent of its graph?

3. Mar 6, 2007

### Gib Z

Find the derivative, and set it equal to the slope of a horizontal line. What is that?

4. Mar 6, 2007

### HallsofIvy

Staff Emeritus
What everyone is saying is "DO IT"! By the way are you really required to use the "quotient difference" formula? It's not too difficult but tedious and most problems like this allow the use of derivative formulas.

5. Mar 6, 2007

### Staff: Mentor

Do you mean, "what is the slope of a horizontal line?"

Draw a graph that shows a horizontal line. Pick two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line. Do you know how to calculate the slope of a line from two points?

6. Mar 7, 2007

### Gib Z

yes thats what i meant, but i knew the answer..set the derivative to zero is what i meant