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## haterofmath 3 years ago find the the rate of change dy/dx where x=x0

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1. haterofmath

\[y=-17; x _{0}=3\]

2. daru

If the function is the constant function y = -17, then the derivative of it (dy/dx) is simply 0. The derivative of any constant is "0". Remember that "derivative" means "the change y with respect to x" in this case. If y = -7 at all points, then it never changes with respect to x. Therefore, the change is 0.

3. haterofmath

so what do you do with the 3

4. amistre64

there has to be more to this question which you have not given us

5. amistre64

if the equation for y is simply: y = -17 .. then daru is correct.

6. haterofmath

sorry wrong problem \[y=6-2x; x_{0}=3\]

7. UnkleRhaukus

?

8. amistre64

first step, is to take the derivative of y, but the method of that step differs depending on how youre spose to go about it. there is a first principals method, and the derivative rules method. Which method have you been doing in your lessons?

9. haterofmath

both

10. amistre64

derivative rules are much easier to work with then; what derivative rule would you say can apply to this question?

11. haterofmath

wouldn't the derivative be 2

12. amistre64

almost, that negative sign (subtraction) needs to be recognized :) y= 6 - 2x y' = 6' - (2x)' = 0 - 2

13. amistre64

now, since there is no place to plug in the value of x in the derivative; the value of the derivative at ANY point is: -2

14. haterofmath

oh ok.

15. haterofmath

/so how do you find that slope of tangent after taking the derivative?

16. amistre64

the value of the derivative DEFINES the slope of the tangent at a given point.

17. amistre64

in this case, 6 - 2x is a straight line whose sloe is -2 at all points

18. haterofmath

so in a problem such as f(x)=5x-3 the slope of the line that is tangent is 5?

19. amistre64

yes

20. amistre64

the more complicated the curve, the less trivial the derivative becomes :) take: y=x^2 y' = 2x the slope at any given point of y=x^2 is defined as 2x the slope at x=3 would be 2(3) = 6 the slope at x=7 would be 2(7) = 14 the slope at x=-2 would be 2(-2) = -4

21. haterofmath

ok. thanks

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