Question

determine tangent line of the curv at (1,1) 4x^2+4xy+4y^2

Answer 1

Isolate for y.
Find the derivative.
Substitue x (1) into your derivative to get your slope.
y = mx + b
m = slope
Sub your point (x,y) in to find b.

Answer 2

would the derivative b= 8x+4x+y'+8y

Answer 3

8x + 4x + 4y + 8y = 12x + 12y therefore y = -x

Answer 4

(4x)(y) is the product rule for finding the derivative. The first x the deriv of the second + the second x the deriv of the first.

Answer 5

y = -1 (slope) therefore y = -1x + b
1 = -1(1) + b
b = 2

therefore y = -x + 2 is your equation of the tangent.

Answer 6

ok can you explain the (4x)(y) part

Answer 7

because the book says the derivative is 4(2x+y)