Question

Find the Equation of the Tangent line to the bullet-nose curve:
y=|x| / sqrt (2-x^2) at the point 1,1

If possible, include the answer with an explanation please. I don't quite understand how to proceed with the calculations.

Answer 1

Since we are finding the tangent line for a positive x, you can change abs(x) to x for simplicity.
dy/dx= (sqrt(2-x^2)+x^2/sqrt(2-x^2))/(2-x^2) -------quotient and chain rule combo
then find the slope of the tangent line when x =1 by plugging in 1 into dy/dx to find dy/dx= 2 when x=1.
now you can make a point-slope equation for the tangent line
y-1=2*(x-1)

Answer 2

Aww you closed it :c