Posted by **Little** on Sunday, February 13, 2011 at 2:47pm.

Consider the curve given by the equation y^3+3x^2y+13=0

a.find dy/dx

b. Write an equation for the line tangent to the curve at the point (2,-1)

c. Find the minimum y-coordinate of any point on the curve.

the work for these would be appreciated i dont need the answers.

- calculus -
**Reiny**, Sunday, February 13, 2011 at 3:11pm
differentiate implicitly.

3y^2 dy/dx + 3x^2 dy/dx + 6xy + 0 = 0

dy/dx(3y^2 + 3x^2) = -6xy

dy/dx/ = -6xy/(3y^2 + 3x^2)

b) sub in x = 2, to get the slope, then use the grade 9 way to find the equation of a line given the slope and a point.

c) set dy/dx = 0

so -6xy = 0

x = 0 or y = 0

when x = 0, y^3 +1 = -13

y = (-13)^(1/3) = appr. - 2.35

when y = 0, 0 + 0 + 13 = 0 , not possible.

so we have one turning point at (0,-2.35)

what about when x becomes large either + or -

investigate for x = 100

y^3 + 30000y = -13

y = -13/30000 which approaches zero.

the same thing is true if x = -100

so the minimum value of y is -2.35 when x = 0

## Answer this Question

## Related Questions

AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

AP AB Calculus - Linear approximation: Consider the curve defined by -8x^2 + 5xy...

calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...

Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...

calculus - Consider line segments which are tangent to a point on the right half...

calculus - 1. Given the curve a. Find an expression for the slope of the curve ...

Calculus - Consider the curve -8x^2+5xy+y^3=-149 1. Find Dy/dx 2. write an ...

calculus - Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) ...

12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...