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Find equations of all tangents to the curve f(x)=9/x that have slope 1
 one year ago
 one year ago
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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ivanmlernerBest ResponseYou've already chosen the best response.0
At first you have to take the derivative of f. Do you understand why is that?
 one year ago

ivanmlernerBest 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?
 one year ago

thuyvyBest 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?
 one year ago

ivanmlernerBest 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?
 one year ago

thuyvyBest 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?
 one year ago

ivanmlernerBest 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.
 one year ago

thuyvyBest 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
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
but the answer that it should be is y=x6 and y = x+6
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
so I must have done something wrong right?
 one year ago

ivanmlernerBest 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
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
What you did so far is correct
 one year ago

thuyvyBest 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?
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
or 3, but yes, thats correct
 one year ago

ivanmlernerBest 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.
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
use slope intercept form now
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
sorry, I'm kinda slow at this point, how do I set this = to 9?
 one year ago

ivanmlernerBest 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
 one year ago

ivanmlernerBest 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.
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
I got it thanks so much for being so patience :)
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
can I ask you something else?
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
same type of problem but it's f(x) = square root of (x+9)
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
slope 1/2 I did the derivatives and solve for x I got x= 1
 one year ago

thuyvyBest 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
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
but the answer should be y=1/4+13/4 where did I do wrong?
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
You got the x wrong.
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
original fx is sqrt(x=9) derivative is 1/2(x+9)^1/2
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
its (1/2)(x+9)^(1/2)
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
Yes i got that.. But solving for x=1
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
Well, thats wrong, did you see the minus, in the exponent?
 one year ago

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

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

thuyvyBest ResponseYou've already chosen the best response.0
the slope is 1/4 not 1/2
 one year ago

ivanmlernerBest 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
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
Can you go from there?
 one year ago

thuyvyBest 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
 one year ago

thuyvyBest 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?
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
I'm almost leaving actually, but I'm here almost every day.
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
quick question on solving this problem \[z(4z+7)  x(4x+7) / (zx)\]
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
I can combine (zx) then cancel top and bottom right?
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
so what is have left is (4z+7) * (4x+7) right?
 one year ago

ivanmlernerBest 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
 one year ago

thuyvyBest ResponseYou've already chosen the best response.0
oh maybe that's why. thanks
 one year ago
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