-
7/25/2019 2.6 PPDay1
1/15
Miss Battaglia
AP Calculus AB/BC
-
7/25/2019 2.6 PPDay1
2/15
Related rate problems
involve fnding the________ at which some
variable changes.
rate
-
7/25/2019 2.6 PPDay1
3/15
For eample! when aballoon is being blown upwith air! both
the
_____________ and the
________________ o" theballoon are changing.
radiusvolume
-
7/25/2019 2.6 PPDay1
4/15
#n each case the rateis a
___________ that has to becomputed given the rateat which some
othervariable! li$e time! is$nown to change.
derivative
-
7/25/2019 2.6 PPDay1
5/15
%o fnd this derivative we write ane&uation that relates the
two
variables. 'e then ____________ both sides o" the e&uation
withrespect to ________ to epress the
derivative we ())* in termso" the derivative we *+,'.
diferentiate
time
-
7/25/2019 2.6 PPDay1
6/15
,"ten the $e- to relatingthe variables in this t-pe o"
problem is DRAWING APICTURE that shows the
geometric relationshipsbetween the variables.
-
7/25/2019 2.6 PPDay1
7/15
. #denti"- and LABELall the given in"o andwhat -ou are as$ed to
fnd. raw a picturei" appropriate.
0. 'rite an )12A%#,+relating the variables.
3. i4erentiateboth sides o" the e&uationwith respect to
TIME.
5. (ubstituteand (olve. (ometimes -ou will
need to use the original e&uation or othere&uations to
solve "or missing parts.
-
7/25/2019 2.6 PPDay1
8/15
6et A be the Area o" a circle o" radius r. 7owis dA/dt related
to dr/dt8
-
7/25/2019 2.6 PPDay1
9/15
6et 9 be the 9olume o" a cube o" side length .7ow is d9/dt
related to d/dt8
-
7/25/2019 2.6 PPDay1
10/15
6et 9 be the 9olume o" a sphere o" radius r. 7ow isd9/dt related
to dr/dt8
-
7/25/2019 2.6 PPDay1
11/15
V=
3 r2
h
-
7/25/2019 2.6 PPDay1
12/15
(uppose and - are both di4erentiable "unctions o" t
and are related b- the e&uation . Find d-/dtwhen :! given
that d/dt:0.
y=x2 +3
-
7/25/2019 2.6 PPDay1
13/15
A pebble is dropped into a calm pond! causing ripples in the"orm
o" concentric circles. %he radius r o" the outer ripple is
increasing at a constant rate o" "t/sec. 'hen the radius is 5"t!
at what rate is the total area A o" the disturbed
waterchanging8
-
7/25/2019 2.6 PPDay1
14/15
Air is being pumped into a spherical balloon at a rate o" 5.;
cubic"t/min. Find the rate o" change o" the radius when the radius
is 0"t.
-
7/25/2019 2.6 PPDay1
15/15
Read 0.! 0?! 0;!
