ind the slope of the tangent line to the curve sqrt(8x+y)+sqrt(8xy)=12 at the point (1,8).

Answer 1

(8x+y)^1/2 + (8xy)^1/2 = 12

1/2 (8x+y) ^-1/2 (8 + y') + 1/2 (8xy) ^-1/2 (8y + 8xy') = 0

At (1,8)

x = 1, y = 8

(16) ^-1/2 (8+y') + (64) ^-1/2 (64 + 8y') = 0

0.25 (8 + y') + 0.125 (64 + 8y') = 0

2 + 0.25y' + 8 + y' = 0

y' = -10 / (1.25) = -8

So y = -8x + c

8 = -8 + c

c = 16

So y = -8x + 16 is the tangent line