EXTRA CREDIT: +5 points
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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