Question

Find the equation of the line tangent to the curve y = 2 - (1/3x) ^ 2 which is perpendicular to the line xy = 0.

Answer 1

Correcting in the last line. x-y=0.

Answer 2

The product of the slope of the perpendicular lines is equal to minus 1

Answer 3

slope for x-y=0 is equal to 1

Answer 4

so the slope of the tangent line would be minus 1

Answer 5

Perpendicular slope = - 1
y = 2 - (1/3x)² = 2 - x²/9
->y' = -2x /9 = -1
=> x= 4.5, y = -4.75
Thus Tangent line at ( 4.5, -4.75) :
y = -x -.25

Answer 6

Thanks

Answer 7

This is the solution

Answer 8

@viniterranova You're unable to post correctly, are you?
Let compare these equations from solution and your post:
y = -(1/3)x² + 2 y = 2 - (1/3x) ^ 2

Answer 9

Anyway, thanks for pointing out that it's YOUR posting problem :)