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thuyvy Group Title

Find equations of all tangents to the curve f(x)=9/x that have slope -1

  • 2 years ago
  • 2 years ago

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  1. ivanmlerner Group Title
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    At first you have to take the derivative of f. Do you understand why is that?

    • 2 years ago
  2. thuyvy Group Title
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    yes I do, I got -9/x2

    • 2 years ago
  3. ivanmlerner Group Title
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    Ok, now what is the meaning of the derivative? Knowing this meaning can you guess what the next step would be?

    • 2 years ago
  4. thuyvy Group Title
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    that is when a function change as the input change, but I'm stuck at the 2nd step what shall I do next? plug in -1 slope as x?

    • 2 years ago
  5. ivanmlerner Group Title
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    Yes, in other words it is the rate of change of a function. But the meaning I was thinking of is the same, but a little diferent. When the input increases in a really small amount, the value changes too. Since those two changes are very small, the rate of change is approximately the change in the value divided by the increase in the input. Do you understand what I just said?

    • 2 years ago
  6. thuyvy Group Title
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    not really, can you lead me into solving this? what is the second step I should take?

    • 2 years ago
  7. ivanmlerner Group Title
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    You need to understand it before gettingg to the next step. But if you want to know, the derivative of a function at x is the slope of its tangent line at this point, that was what I was trying to show you. Then, you should put -9/x2=-1, that is the slope, to find in which points the line passes.

    • 2 years ago
  8. thuyvy Group Title
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    Yes I got to this step, when I was trying to solve for x I got +- 3

    • 2 years ago
  9. thuyvy Group Title
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    but the answer that it should be is y=-x-6 and y = -x+6

    • 2 years ago
  10. thuyvy Group Title
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    so I must have done something wrong right?

    • 2 years ago
  11. ivanmlerner Group Title
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    Wait, you just found out one point in wich the line passes, it is not the answer yet

    • 2 years ago
  12. ivanmlerner Group Title
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    What you did so far is correct

    • 2 years ago
  13. thuyvy Group Title
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    oh ic okay, so the other point is 3 since 9/x = y and x is 3 therefore y = 3 right?

    • 2 years ago
  14. ivanmlerner Group Title
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    or -3, but yes, thats correct

    • 2 years ago
  15. thuyvy Group Title
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    so now what's next?

    • 2 years ago
  16. ivanmlerner Group Title
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    Now, you know a point that belongs to the line, and its slope. The general formula for a line is y=ax+b, and you alrady have a, now put the point you know that belongs to it, and you will find b.

    • 2 years ago
  17. FaisalAyaz Group Title
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    use slope intercept form now

    • 2 years ago
  18. thuyvy Group Title
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    y = mx+b --> -3=-1x+b

    • 2 years ago
  19. thuyvy Group Title
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    sorry, I'm kinda slow at this point, how do I set this = to 9?

    • 2 years ago
  20. ivanmlerner Group Title
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    You dont need to, you know x and y, from the points (-3, -3) and (3, 3) that this tangent passes through, and you know a. Now: -3=-1*(-3)+b1 3=-1*3+b2

    • 2 years ago
  21. thuyvy Group Title
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    oh okay

    • 2 years ago
  22. thuyvy Group Title
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    I got it from here

    • 2 years ago
  23. ivanmlerner Group Title
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    Before, you found out in which points the tangent have this slope, then, you found out the value of the function at this point, and now you use those information to get the formulas for the tangent lines. You seem a little bit confused with what the numbers you are getting mean.

    • 2 years ago
  24. thuyvy Group Title
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    I got it thanks so much for being so patience :)

    • 2 years ago
  25. ivanmlerner Group Title
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    Your welcome

    • 2 years ago
  26. thuyvy Group Title
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    can I ask you something else?

    • 2 years ago
  27. ivanmlerner Group Title
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    Of course

    • 2 years ago
  28. thuyvy Group Title
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    same type of problem but it's f(x) = square root of (x+9)

    • 2 years ago
  29. thuyvy Group Title
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    slope 1/2 I did the derivatives and solve for x I got x= -1

    • 2 years ago
  30. thuyvy Group Title
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    I plugged x= -1 back to original equation I got y = +/- 2 sqrt 2 then I use slope intercept to find equations, I got y= 1/4+9/4 sqrt 2

    • 2 years ago
  31. thuyvy Group Title
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    but the answer should be y=1/4+13/4 where did I do wrong?

    • 2 years ago
  32. ivanmlerner Group Title
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    You got the x wrong.

    • 2 years ago
  33. ivanmlerner Group Title
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    Or the derivative

    • 2 years ago
  34. thuyvy Group Title
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    original fx is sqrt(x=9) derivative is 1/2(x+9)^1/2

    • 2 years ago
  35. thuyvy Group Title
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    Where did I do wrong.

    • 2 years ago
  36. ivanmlerner Group Title
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    its (1/2)(x+9)^(-1/2)

    • 2 years ago
  37. thuyvy Group Title
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    Yes i got that.. But solving for x=-1

    • 2 years ago
  38. ivanmlerner Group Title
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    Well, thats wrong, did you see the minus, in the exponent?

    • 2 years ago
  39. thuyvy Group Title
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    No i said that mine is 1/{2(x+9)^1/2 same thing

    • 2 years ago
  40. ivanmlerner Group Title
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    \[\frac{ 1 }{ 2 }=\frac{ 1 }{ 2\sqrt{x+9} }\rightarrow \sqrt{x+9}=1\rightarrow x+9=\pm1\rightarrow x=-10 or -8\]

    • 2 years ago
  41. thuyvy Group Title
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    the slope is 1/4 not 1/2

    • 2 years ago
  42. ivanmlerner Group Title
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    sorry, didnt ssee you posting. Then the left side of the equation will be 1/4, and sqrt(x+9)=2 and x+9=+-4, wich gives us: x=-5, and x=-13

    • 2 years ago
  43. ivanmlerner Group Title
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    Can you go from there?

    • 2 years ago
  44. thuyvy Group Title
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    let me try to do calculation, I did the calculation but got +/- 2 sqrt 2.. give me 1 minute please

    • 2 years ago
  45. ivanmlerner Group Title
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    Sure

    • 2 years ago
  46. thuyvy Group Title
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    I got it, I think I got messed up when I was trying to square to get rid of sq rt. Thanks Do you have time to help me on other problems?

    • 2 years ago
  47. ivanmlerner Group Title
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    I'm almost leaving actually, but I'm here almost every day.

    • 2 years ago
  48. thuyvy Group Title
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    quick question on solving this problem \[z(4z+7) - x(4x+7) / (z-x)\]

    • 2 years ago
  49. thuyvy Group Title
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    I can combine (z-x) then cancel top and bottom right?

    • 2 years ago
  50. thuyvy Group Title
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    so what is have left is (4z+7) * (4x+7) right?

    • 2 years ago
  51. ivanmlerner Group Title
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    No, be carefull, think of what is being divided, when you have something that is not being divided you cannot sum them withou a common denominator

    • 2 years ago
  52. thuyvy Group Title
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    oh maybe that's why. thanks

    • 2 years ago
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