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thuyvy

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

  • one year ago
  • one year ago

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

    • one year ago
  2. thuyvy
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    yes I do, I got -9/x2

    • one year ago
  3. ivanmlerner
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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?

    • one year ago
  4. thuyvy
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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?

    • one year ago
  5. ivanmlerner
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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?

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

    • one year ago
  7. ivanmlerner
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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.

    • one year ago
  8. thuyvy
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    Yes I got to this step, when I was trying to solve for x I got +- 3

    • one year ago
  9. thuyvy
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    but the answer that it should be is y=-x-6 and y = -x+6

    • one year ago
  10. thuyvy
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    so I must have done something wrong right?

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

    • one year ago
  12. ivanmlerner
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    What you did so far is correct

    • one year ago
  13. thuyvy
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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?

    • one year ago
  14. ivanmlerner
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    or -3, but yes, thats correct

    • one year ago
  15. thuyvy
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    so now what's next?

    • one year ago
  16. ivanmlerner
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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.

    • one year ago
  17. FaisalAyaz
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    use slope intercept form now

    • one year ago
  18. thuyvy
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    y = mx+b --> -3=-1x+b

    • one year ago
  19. thuyvy
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    sorry, I'm kinda slow at this point, how do I set this = to 9?

    • one year ago
  20. ivanmlerner
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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

    • one year ago
  21. thuyvy
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    oh okay

    • one year ago
  22. thuyvy
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    I got it from here

    • one year ago
  23. ivanmlerner
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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.

    • one year ago
  24. thuyvy
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    I got it thanks so much for being so patience :)

    • one year ago
  25. ivanmlerner
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    Your welcome

    • one year ago
  26. thuyvy
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    can I ask you something else?

    • one year ago
  27. ivanmlerner
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    Of course

    • one year ago
  28. thuyvy
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    same type of problem but it's f(x) = square root of (x+9)

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

    • one year ago
  30. thuyvy
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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

    • one year ago
  31. thuyvy
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    but the answer should be y=1/4+13/4 where did I do wrong?

    • one year ago
  32. ivanmlerner
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    You got the x wrong.

    • one year ago
  33. ivanmlerner
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    Or the derivative

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

    • one year ago
  35. thuyvy
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    Where did I do wrong.

    • one year ago
  36. ivanmlerner
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    its (1/2)(x+9)^(-1/2)

    • one year ago
  37. thuyvy
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    Yes i got that.. But solving for x=-1

    • one year ago
  38. ivanmlerner
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    Well, thats wrong, did you see the minus, in the exponent?

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

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

    • one year ago
  41. thuyvy
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    the slope is 1/4 not 1/2

    • one year ago
  42. ivanmlerner
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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

    • one year ago
  43. ivanmlerner
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    Can you go from there?

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

    • one year ago
  45. ivanmlerner
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    Sure

    • one year ago
  46. thuyvy
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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?

    • one year ago
  47. ivanmlerner
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    I'm almost leaving actually, but I'm here almost every day.

    • one year ago
  48. thuyvy
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    quick question on solving this problem \[z(4z+7) - x(4x+7) / (z-x)\]

    • one year ago
  49. thuyvy
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    I can combine (z-x) then cancel top and bottom right?

    • one year ago
  50. thuyvy
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    so what is have left is (4z+7) * (4x+7) right?

    • one year ago
  51. ivanmlerner
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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

    • one year ago
  52. thuyvy
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    oh maybe that's why. thanks

    • one year ago
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