Question

Find the function y = y(x) such that the line tangent to the graph of y = y(x) at (x, y) intersects the x-axis at x/2 .

Answer 1

i know i have to end up with dy/dx = something but i cant figure out how to get there with this clue... any suggestions?

Answer 2

Well, dy/dx is the gradient at a specific point of a curve.

Answer 3

ok, so i need to find the equation of the tangent line

Answer 4

tangent line
\[y-y_1 = m(x-x_1)\]
\[m = \frac{dy}{dx}\]
line crosses point (x/2 , 0)
\[-y_1 = \frac{dy}{dx}(\frac{x_1}{2}-x_1)\]
from here you can set up diff equ and separate variables to solve for y(x)

Answer 5

Got you, I see where im going now. The only thing im not sure about is the sign on y. Are u positive is negative?

Answer 6

im meant y being negative...

Answer 7

yes because the line is tangent to curve at (x_1, y_1)
the "y" value of line is 0 at x intercept
0 - y_1 = -y_1

Answer 8

Got it. So i solved it and got: \[y(x) = x^2 +C\] What do you think?

Answer 9

yep well close, i get constant in front
y = Cx^2

Answer 10

ahhhhh, yes. Because 2lnx + C becomes the exponent for e and e^C becomes C

Answer 11

haha yeah was just going to say that :)

Answer 12

I always mess up whenever e or ln are involved

Answer 13

Thank you for your help, you got me out of a pickle :)

Answer 14

no problem