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

  2. daru
    • 3 years ago
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    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
    • 3 years ago
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    so what do you do with the 3

  4. amistre64
    • 3 years ago
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    there has to be more to this question which you have not given us

  5. amistre64
    • 3 years ago
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    if the equation for y is simply: y = -17 .. then daru is correct.

  6. haterofmath
    • 3 years ago
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    sorry wrong problem \[y=6-2x; x_{0}=3\]

  7. UnkleRhaukus
    • 3 years ago
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    ?

  8. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    both

  10. amistre64
    • 3 years ago
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    derivative rules are much easier to work with then; what derivative rule would you say can apply to this question?

  11. haterofmath
    • 3 years ago
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    wouldn't the derivative be 2

  12. amistre64
    • 3 years ago
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    almost, that negative sign (subtraction) needs to be recognized :) y= 6 - 2x y' = 6' - (2x)' = 0 - 2

  13. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    oh ok.

  15. haterofmath
    • 3 years ago
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    /so how do you find that slope of tangent after taking the derivative?

  16. amistre64
    • 3 years ago
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    the value of the derivative DEFINES the slope of the tangent at a given point.

  17. amistre64
    • 3 years ago
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    in this case, 6 - 2x is a straight line whose sloe is -2 at all points

  18. haterofmath
    • 3 years ago
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    so in a problem such as f(x)=5x-3 the slope of the line that is tangent is 5?

  19. amistre64
    • 3 years ago
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    yes

  20. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    ok. thanks

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