Question

Use Implicit Differentiation to find first dy/dx , then the equation of the tangent line to the curve x2+xy+y2= 2-y at the point (0,-2)

b. Determine a function of the form f(x)= ax2+ bx + c (that is, find the real numbers a,b,c ) if the graph of the function has slope 2 at the point (3,4) , and has a horizontal tangent where x=1

c. Assume that x,y are functions of variable t satisfying the equation x2+xy=10. Find dy/dt when x=2 if dx/dt = -1

Thank you so much!!!

Answer #1

Use implicit differentiation to find an equation of the tangent
line to the curve at the given point.
x2+y2=(2x2+4y2-x)2
(0, 0.25)
(cardioid)
y=?

Use implicit differentiation to find an equation of the tangent
line to the curve at the given point. 3(x2 + y2)2 = 25(x2 − y2) (2,
1) (lemniscate) y= ?

A) Use implicit differentiation to find an equation of the
tangent line to the ellipse defined by
5x^2+4xy+3y^2=12 at the point (−1,−1)
B) Find dy/dx by implicit differentiation, if ey=2x−2y

Consider x^2 +sin(y)=4xy^2 +1
a.)Use Implicit differentiation to find dy/dx
b.) find an equation tangent of the line to the curve x^2
+sin(y)=4xy^2 +1 at (1,0)

Using implicit differentiation complete the following:
A) Find dy/dx of x^3 + y^3 =4xy
B) Find the equation of the tangent line to the curve at the
point (1,1) in slope-intercept form
C) Find the equation of the normal line to the curve at the
point (1,1) in slope- intercept form

3. Consider the equation:
x^2y −√y = 2 + 4x^2
a) Find dy/dx using implicit differentiation. b)Construct the
equation of the tangent line to the graph of this equation at the
point (1, 9)

Use implicit differentiation to find dy dx for x^2 y^3 + 3y^2 −
5x = −10.
(b) Find the equation of the line tangent to the curve in part
a) at the point (1, 2).

1. Find the equation of the tangent line to the graph of ?2? −
5??2 + 6 = 0 at (3,1).
2.. Find the equation of the normal line to the graph of sin(??) =
? at the point (?/2 ,1).
3.. Find the equation of the tangent line to the graph of cos(??) =
? at the point (0.1)
Find implicit differentiation of dy/dx
a) xy=x+y
b) xcosy=y
c)x^3 +y^2=0

Use implicit differentiation to determine dy/dx given the
equation e^x⋅y^3+x^4=sin(y)
dy/dx=

4) Use implicit differentiation to find the equation of the
tangent line to the curve xy^3+xy=16 at the point (8,1). The
equation of this tangent line can be written in the form
y=mx+by=mx+b where m is:
and where b is:

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