Question

Find the slope of the tangent line to the graph of -2y + 8x^2 = -7x + 9y^2 - 29 at (2,-3)

Answer 1

Explanation:

Take the derivative of all terms with respect to x:

-2(dy/dx) + 16x = -7 + 18y(dy/dx). Grouping the (dy/dx) terms on the left, we get:

(dy/dx)(-2 - 18y) = -7 - 16x, or

-7 - 16x

dy/dx = ------------------

-2(1 + 18y)

Substituting 2 for x and -3 for y, we obtain the desired derivative:

-7 - 16x -7 - 32 -39

dy/dx = ------------------ = --------------- = ----------- = -0.368

-2(1 + 18y) -2(1 - 54) 106