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anonymous
 5 years ago
Determine the equations of both lines that are tangent to the graph of f(x) = x^2 and pass through the point (1,3).
anonymous
 5 years ago
Determine the equations of both lines that are tangent to the graph of f(x) = x^2 and pass through the point (1,3).

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1f'(x)=2x f'(a)=2a so the equation of the line is y=2ax+b we know a point on this line (1,3) so we 3=2a(1)+b 3=2a+b ....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0One would have a negative slope, the other would be positive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Would those two lines be orthogonal to each other?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1that looks possible it looks like it could form a 90 degree angles

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok so then they must have reciprocal slopes

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1opposite reciprocal slopes

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1wait i htink i'm fixing to figure something out....

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1now we need to figure the y intercept for each line which is easy since we know a point on both lines. both lines have the point (1,3)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1y=6x+b (1,3) 3=6(1)+b 3=6+b 36=b 9=b so y=6x9 is the line that is tangent to the point (3,9) on the curver y=x^2 that passes through (1,3) y=2x+b (1,3) 3=2(1)+b 3+2=b 1=b so y=2x1 is the line tangent to the point (1,1) on the curve y=x^2 that passes through (1,3)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1we can check if you want Let's find the tangent line at (3,9) and see if passes through (1,3) so f'(x)=2x f'(3)=6 y=6x+b 9=6(3)+b 918=b b=9 so y=6x9 is (1,3) on that line 3=6(1)9=3 so yes! now let's check the tangent line at (1,1) and see if passes through (1,3) so f'(x)=2x f'(1)=2 y=2x+b 1=2+b b=1 y=2x+1 is (1,3) on that line 3=2(1)+1=3 so yes! :) we are finished!

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so the lines arent orthogonal

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1do you have any questions?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Why did you choose the general points (a,a^2) to be X1,Y1 respectively? Does it make a difference if I were to use them as X2,Y2 in the slope formula?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1(a^2(3))/(a1)=(3a^2)/(1a) we can make both sides look the same (1)/(1)=1 so if we multiply our second fraction by (1)/(1) we would get the first fraction or vice versa

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1(y1y2)/(x1x2)=(y2y1)/(x2x1) (1)/(1)*(y1y2)/(x1x2)=(y2y1)/(x2x1)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1ab is the same as (ba)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1(62)/(31)=4/2=2 (26)/(13)=4/(2)=2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes thank you very much. I have just a few more questions if you don't mind helping me out with them.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If f(a) = 0 and f'(a) = 6, find the limit h > 0 of: f(a + h)  2h

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1i got it scanning it now

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1i just used the definition of derivative

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1and plugged and what they gave me and solved for limh>0 (f(a+h)/(2a))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1do you understand both problems we did?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1oops solved for limh>0(f(a+h)/(2h))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't understand how you did the second question.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1what is definition of the derivative at a of f

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Wait, ok wouldn't it be 12 for the answer because: 6 = f(a+h)/h * (1/2) 6(2) = f(a+h)/h

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry I don't know what happened

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1doesn't the question above ask for lim h>0 (f(a+h)/(2a))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1oops the bottom is suppose to read 2h

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so we have 6=limh>0(f(a+h)/(2h))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1oops 6=limh>0(f(a+h)/h) do you understand this far?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1ok but the want 1/2* limh>0(f(a+h)/h) so if we multiply the above equation on one side by 1/2 don't we have to do it to the other side?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok last question for now is this: Determine the value of "a', given that the line "ax  4y + 21 = 0" is tangent to the graph y = a/x^2 at x = 2

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1if you write that tangent line in y=mx+b form we can find the slope of the line

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so the equation of that line can be written y=ax/421/4 where a/4 is the slope of this tangent line

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The slope of the line is a right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so then we equate the two equations together

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so you are talking about finding the derivative of that function y=a/x^2 at x=2 and then setting that equal to the slope of tangent line and solving for a? that's what I'm working on right now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes and I got 7 when equating the two equations together. But I don't understand how we can equate a y with a y' (derivative)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so we get a=a so this equation holds for any a is what I get

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh so you are making them equal to each other by solving for a?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a = , a =, and then equating them?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1derivative means slope this slope is suppose to be the same as the slope tangent to whatever point we are talkng about so we can find the slope of the tangent line and find the derivative of the curve at the given point and set them equal to find what a should be but the resulting equation is a=a this equation holds for every number 3=3 4=4 it is never not true

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1a/4=2a/(x^3) at x=2 is what I did

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1a/4 is the slope of the tangent line

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OOHHHH I understand So we can take a/4 to be the slope, which must be the same as the graph's slope at that point?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1right just like the very very question we did sort of

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Got it. Thank you so much for your help. I have to go now. I really appreciate you taking your time to do this for me.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1no problem become my fan :)
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