Question

Examine the function f(x)=x+(3/x). Find the point on the curve at which the tangent lines pass through the point (1, 1).

Answer 1

@byerskm2 Hi,

\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

Do you know how to find the slope of tangent to any curve f(x) ?

Answer 2

Yes, I know the derivative is 1- 3/x^2
and the tangent line touching (1,1) is -2x+3
but then I got stuck

Answer 3

How do I find the point on the the function line where the tangent line touches?

Answer 4

u need to solve the equation of curve y=x+3/x and y=-2x+3 simultaneously

Answer 5

when you say simultaneous do you mean set them equal to each other and solve for x?

Answer 6

the slope would be 2 because we treat the (1,1) as the 0 point right?

Answer 7

oh yes, we put x=1 in 1-3/x^2 to get slope
=1-3/1 =1-3 = -2
so slope is actually -2
get this ?

Answer 8

and yes your equation y=-2x+3 is correct,
now i said to equate the two curve equation to get the intersection points
so
-2x+3 = x+3/x
can u find values of x from here ?

Answer 9

x=0 and x=-1
so which is the correct answer?

Answer 10

x is not 0
-2x^2 +3x=x^2+3
so
3x^2 -3x + 3 =0
or
x^2-x+1 =0
solve this quadratic equation to get the values of x

Answer 11

x=1

Answer 12

that equation doesn't seem to have real roots.
can u please verify your question ?

Answer 13

This is the question. I hit the exact same wall but when I gave DNE as the answer it was incorrect and now I just don't know what to do!
:(

Answer 14

the line -2x+3 and curve x+3/x do not intersect.

Answer 15

so this question is impossible? They wouldn't give me an impossible question
Grrrr

Answer 16

i will try to go through this again, if i come up with something else, i will let you know

Answer 17

Thanks a bunch!