Question

 

part 1)

Find dy/dx by implicit differentiation.

3x^6+x^5y−2xy^6=8

dy/dx=

part 4)

A campground owner has 2000 meters of fencing. She wants to enclose a rectangular field bordering a lake, with no fencing needed along the lake: see the sketch.

a) Write an expression for the length of the field: 2000-x (this is correct)

b) Find the area of the field (length times width): -x^2+2000x (this is correct)

c) Find the value of x leading to the maximum area:

d) Find the maximum area:

I got (2y^6-5yx^4-30x^5)/(x^5-12xy^5)

part 2)

sqrt (x+y)=9+x^2y^2

dy/dx= (80+4x^3y^4+36xy^2)/(1-4x^4y^3-36x^2y)

part 3)

Use implicit differentiation to find an equation of the tangent line to the curve

sin(x+y)=6x−6y at the point (π,π).

Tangent Line Equation: y= (5x/7)-(2pi/7)

Answer 1