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Ch 3 - Day 4 AP Calculus BC Name:

Implicit Differentiation Review

NO CALCULATOR!!!

For each implicit function, find [pic].

1. [pic]

2. [pic]

3. [pic]

4. Find the equation of the line tangent to the graph of [pic] when [pic].

(A) [pic]

(B) [pic]

(C) [pic]

(D) [pic]

(E) [pic]

5. Consider the curve given by [pic] .

a) Find all coordinates, ( x , y ), where the curve has a horizontal tangent.

b) When x = ̶ 5, find the y-coordinate such that the curve has a vertical tangent.

6. Consider the curve given by [pic] .

a) When y = [pic], find the x-coordinate such that the slope of the curve is undefined.

b) Find [pic] and [pic] at the point ( 1 , 2 ).

c) Does f have a relative minimum, a relative maximum, or neither at ( 1 , 2 )? Justify your answer.

7. Consider the differential equation [pic] .

a) Find [pic] in terms of x and y . Describe the region in the x y – plane in which all the solution curves to the differential equation are concave up.

b) Let [pic] be a particular solution to the differential equation with the initial condition [pic]. Does f have a relative minimum, a relative maximum, or neither at x = 0 ? Justify your answer.

The remaining problems are review. No calculator allowed!

8. Determine local maxima or minima of [pic].

9. Determine local maxima or minima of [pic].

10. The position function for a particle’s motion on a line is [pic], [pic].

At what value(s) of t is the particle at rest?

(A) [pic]

(B) [pic]

(C) [pic] and [pic]

(D) [pic]

(E) no value of t

11. [pic] has

I a relative minimum at [pic]

II a horizontal asymptote [pic]

III a vertical asymptote [pic]

(A) I only

(B) I and II

(C) I and III

(D) II and III

(E) I, II, and III

12. For what value(s) of x are the lines tangent to [pic] and [pic] parallel?

(A) [pic] and [pic]

(B) [pic] only

(C) [pic] only

(D) [pic] only

(E) [pic] only

-----------------------

ANSWERS:

1) [pic] 5a) none b) ̶ 1 7a) [pic]; all ( x , y ) [pic] [pic] 8) min at [pic] , no local max

2) [pic] 6a) [pic] b) rel min, since [pic] and [pic] 9) min at x = 3, max at x = -3

3) [pic] b) 0; [pic] 10) B

4) A c) rel min, since [pic] and [pic] 11) C

12) A

(2nd Derivative Test)

(2nd Derivative Test)

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