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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
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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ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
At first you have to take the derivative of f. Do you understand why is that?
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
yes I do, I got 9/x2
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Ok, now what is the meaning of the derivative? Knowing this meaning can you guess what the next step would be?
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
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

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
not really, can you lead me into solving this? what is the second step I should take?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
Yes I got to this step, when I was trying to solve for x I got + 3
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
but the answer that it should be is y=x6 and y = x+6
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
so I must have done something wrong right?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Wait, you just found out one point in wich the line passes, it is not the answer yet
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
What you did so far is correct
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
oh ic okay, so the other point is 3 since 9/x = y and x is 3 therefore y = 3 right?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
or 3, but yes, thats correct
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
so now what's next?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
use slope intercept form now
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
y = mx+b > 3=1x+b
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
sorry, I'm kinda slow at this point, how do I set this = to 9?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
I got it from here
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
I got it thanks so much for being so patience :)
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Your welcome
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
can I ask you something else?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Of course
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
same type of problem but it's f(x) = square root of (x+9)
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
slope 1/2 I did the derivatives and solve for x I got x= 1
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
but the answer should be y=1/4+13/4 where did I do wrong?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
You got the x wrong.
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Or the derivative
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
original fx is sqrt(x=9) derivative is 1/2(x+9)^1/2
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
Where did I do wrong.
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
its (1/2)(x+9)^(1/2)
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
Yes i got that.. But solving for x=1
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Well, thats wrong, did you see the minus, in the exponent?
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
No i said that mine is 1/{2(x+9)^1/2 same thing
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ 1 }{ 2 }=\frac{ 1 }{ 2\sqrt{x+9} }\rightarrow \sqrt{x+9}=1\rightarrow x+9=\pm1\rightarrow x=10 or 8\]
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
the slope is 1/4 not 1/2
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
Can you go from there?
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
let me try to do calculation, I did the calculation but got +/ 2 sqrt 2.. give me 1 minute please
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
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

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
I'm almost leaving actually, but I'm here almost every day.
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
quick question on solving this problem \[z(4z+7)  x(4x+7) / (zx)\]
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
I can combine (zx) then cancel top and bottom right?
 2 years ago

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
so what is have left is (4z+7) * (4x+7) right?
 2 years ago

ivanmlerner Group TitleBest ResponseYou've already chosen the best response.0
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

thuyvy Group TitleBest ResponseYou've already chosen the best response.0
oh maybe that's why. thanks
 2 years ago
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