## steve816 one year ago Can someone give me a link that explains about difference quotient? Thanks!

2. FireKat97

3. FireKat97

4. Empty

5. steve816

Thanks everyone for the link guys. My teacher is so bad at time management and explaining that I pretty much have to teach myself stuff.

6. anonymous

I felt that way in college for a lot of the classes, having to teach myself the material.

7. anonymous

the difference quotient is essentially the slope between the points (x, f(x) ) and ( x + h, f( x +h) )

8. anonymous

|dw:1442911973354:dw|

9. anonymous

|dw:1442912055335:dw|

10. anonymous

x+ h - x = h that is why you will get h in the denominator

11. anonymous

$$\Large \sf slope = \frac{rise}{ run} =\frac{f(x+h) - f(x) }{(x+h) - x }= \frac{f(x+h) - f(x) }{h}$$

12. anonymous

if you let h go to zero, then you have the derivative at x . so the derivative at x is the limit of the slope as h goes to zero. we also call this the 'instantaneous slope' , since it is the slope at the instant of time x.