Calculus Question

Question

Find the slope of the curve 8x²+y²-2x+4y=270 at the point (-5,6). Round the answer to the nearest thousandth. 

 

Help!?

Answer 1

Use implicit differentiation.

 

16x + 2yy' - 2 + 4y' = 0

 

 

Move all the non-y' terms to the right side of equation.

 

2yy' + 4y' = -16x + 2

 

y' (2y + 4) = -16x + 2

 

y' = (-16x + 2) / (2y + 4)

 

 

Next, evaluate y' when x=-5 and y=6.