Question

Find the slope of the tangent line to the curve
4x^2-2xy+2y^3=94
at the point (4,3) .

Answer 1

Find the derivative and then plug in x = 4 and y = 3. That will be your slope of the tangent line to the given curve.

Answer 2

This involved implicit differentiation.

Answer 3

i found the derivative, but it wasn't right still?

Answer 4

after differentiating
\[8x-2y-2x \frac{dy}{dx}+6y^{2} \frac{dy}{dx} = 94\]
solving
\[\frac{dy}{dx} = \frac{2y-8x+94}{6y^{2}-2x}\]
plug in point (4,3)
\[\frac{dy}{dx} = \frac{34}{23}\]