first cross-multiply
y + y x^2 = x
dy/dx + y(2x) + 2x dy/dx = 1
dy/dx(1 + 2x) = 1 - 2xy
dy/dx = (1-2xy)/(1+2x)
at (4, 1/4)
dy/dx = (1 - 2(4)(1/4))/(1 + 2(4))
= -1/9
equation of tangent:
y = (-1/9)x + b
at (4,1/4)
1/4 = (-1/9)(4) + b
b = 5/9
equation is y = (-1/9)x + 5/9
slope = -1/9
y-intercept is 5/9
Why would you round off and create inaccuracy, while the above gives you exact values.
BTW, just noticed this same question 3 years ago here
http://www.jiskha.com/display.cgi?id=1320285563
(I answered it by taking the derivative directly, and they changed the y value of the given point)
The curve y = x/(1 + x^2)is called a serpentine. Find an equation of the tangent line to this curve at the point (4, 0.24).
Round the slope and y-intercept to two decimal places.)
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