Given the equation of the curve 2x2 -3xy +y= 10, find dy/dx at the point (0, 10).

Answer 1

2x² - 3xy + y = 10

4x - 3[ x(dy/dx) + (1)y ] + (dy/dx) = 0

Since (0,10) is on the curve, we have 4(0) - 3[ 0(dy/dx) + (1)(10) ] + dy/dx = 0

So, dy/dx = 30.

Answer 2

This is an Implicit Differentiation problem.

Differentiate the equation with respect to x, treat y as y(x), and solve the resulting equation for y'(x).

Then plug in the given point x = 0, y = 10 to find the value of y'(x) at that point.