## thuyvy Group Title Find equations of all tangents to the curve f(x)=9/x that have slope -1 one year ago one year ago

1. ivanmlerner Group Title

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

2. thuyvy Group Title

yes I do, I got -9/x2

3. ivanmlerner Group Title

Ok, now what is the meaning of the derivative? Knowing this meaning can you guess what the next step would be?

4. thuyvy Group Title

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?

5. ivanmlerner Group Title

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?

6. thuyvy Group Title

not really, can you lead me into solving this? what is the second step I should take?

7. ivanmlerner Group Title

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.

8. thuyvy Group Title

Yes I got to this step, when I was trying to solve for x I got +- 3

9. thuyvy Group Title

but the answer that it should be is y=-x-6 and y = -x+6

10. thuyvy Group Title

so I must have done something wrong right?

11. ivanmlerner Group Title

Wait, you just found out one point in wich the line passes, it is not the answer yet

12. ivanmlerner Group Title

What you did so far is correct

13. thuyvy Group Title

oh ic okay, so the other point is 3 since 9/x = y and x is 3 therefore y = 3 right?

14. ivanmlerner Group Title

or -3, but yes, thats correct

15. thuyvy Group Title

so now what's next?

16. ivanmlerner Group Title

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.

17. FaisalAyaz Group Title

use slope intercept form now

18. thuyvy Group Title

y = mx+b --> -3=-1x+b

19. thuyvy Group Title

sorry, I'm kinda slow at this point, how do I set this = to 9?

20. ivanmlerner Group Title

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

21. thuyvy Group Title

oh okay

22. thuyvy Group Title

I got it from here

23. ivanmlerner Group Title

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.

24. thuyvy Group Title

I got it thanks so much for being so patience :)

25. ivanmlerner Group Title

26. thuyvy Group Title

can I ask you something else?

27. ivanmlerner Group Title

Of course

28. thuyvy Group Title

same type of problem but it's f(x) = square root of (x+9)

29. thuyvy Group Title

slope 1/2 I did the derivatives and solve for x I got x= -1

30. thuyvy Group Title

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

31. thuyvy Group Title

but the answer should be y=1/4+13/4 where did I do wrong?

32. ivanmlerner Group Title

You got the x wrong.

33. ivanmlerner Group Title

Or the derivative

34. thuyvy Group Title

original fx is sqrt(x=9) derivative is 1/2(x+9)^1/2

35. thuyvy Group Title

Where did I do wrong.

36. ivanmlerner Group Title

its (1/2)(x+9)^(-1/2)

37. thuyvy Group Title

Yes i got that.. But solving for x=-1

38. ivanmlerner Group Title

Well, thats wrong, did you see the minus, in the exponent?

39. thuyvy Group Title

No i said that mine is 1/{2(x+9)^1/2 same thing

40. ivanmlerner Group Title

$\frac{ 1 }{ 2 }=\frac{ 1 }{ 2\sqrt{x+9} }\rightarrow \sqrt{x+9}=1\rightarrow x+9=\pm1\rightarrow x=-10 or -8$

41. thuyvy Group Title

the slope is 1/4 not 1/2

42. ivanmlerner Group Title

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

43. ivanmlerner Group Title

Can you go from there?

44. thuyvy Group Title

let me try to do calculation, I did the calculation but got +/- 2 sqrt 2.. give me 1 minute please

45. ivanmlerner Group Title

Sure

46. thuyvy Group Title

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?

47. ivanmlerner Group Title

I'm almost leaving actually, but I'm here almost every day.

48. thuyvy Group Title

quick question on solving this problem $z(4z+7) - x(4x+7) / (z-x)$

49. thuyvy Group Title

I can combine (z-x) then cancel top and bottom right?

50. thuyvy Group Title

so what is have left is (4z+7) * (4x+7) right?

51. ivanmlerner Group Title

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

52. thuyvy Group Title

oh maybe that's why. thanks