A
(1+x)y^3 + (x^4)y - 85 = 0
y^3 + 3(1+x)y^2y' + 4x^3y + x^4y' = 0
y' = -(y^3+4x^3y)/(3(1+x)+x^4)
= -(y^3+4x^3y)/(x^4+3x+3)
B
y'(3) = -109/93
So, the tangent line is
y-1 = -109/93 (x-3)
C
y(3) = 1, so g(1) = 3
g'(1) = 1/y'(3) = -93/109
Consider a curve given implicitly by the equation (1+x)y^3 + (x^4)y - 85 = 0.
A. Calculate dy/dx at a general point (x,y).
B. Write the equation of the tangent line to the curve at the point (3,1).
C. At (3,1), y(x) is defined implicitly as a function of x. Let g(x) be the inverse function of y(x). Compute g'(1).
1 answer
1 answer