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2.9  Implicit Differentiation

1) Use implicit differentiation to find    if  x3 + y3 = 6xy.

A)

B)

C)

D)

E)

2) Find   if y3 + y2 – 5y – x2 = -4.

A) –

B)

C)

D) –

E) none of the above

3) Find the slope of the curve  + = 9  at the point (1, 16).

A) 2

B) -2

C)

D) –

E) 1

4) Find the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (, – ).

A)

B) –

C) 1

D) 0

E) -1

5) Find an equation of the line tangent to the curve  2xy2 + x2y =  6  at the point  (1, – 2).

A) 4x – 7y = 18

B) 4x + 7y = -10

C) 7x + 4y = -1

D) 7x – 4y = 15

E) none of the above

6) Find the slope  of the curve  tan(2x + y) = x  at  (0, 0).

A) 1

B) 2

C) -2

D) -1

E) 0

7) If x sin y = cos (x + y), then calculate .

A) –

B)

C) –

D)

E)

8) Find all points on the graph x2 + y2 = 4x + 4y at which the tangent line is horizontal.

A) (2,  2 – ) and (2, 2 + )

B) (1,  2 – ) and (2, 2 + )

C) (2,  2 – ) and (1, 2 + )

D) (0, 0)  and  (0, 4)

E) The tangent line is never horizontal.

9) Given the curve x3 + y3 = 9xy,  find (a) the equation of its tangent line at the point (2, 4) and (b) the equation of its tangent line with slope -1.

10) Show that the curves given by  y2 + 4y + 4x + 3 = 0  and y2 = 4x + 1  have a common tangent line and determine its equation.

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