2.6 ppday1
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Miss Battaglia
AP Calculus AB/BC
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Related rate problems
involve fnding the________ at which some
variable changes.
rate
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For eample! when aballoon is being blown upwith air! both the
_____________ and the
________________ o" theballoon are changing.
radiusvolume
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#n each case the rateis a
___________ that has to becomputed given the rateat which some othervariable! li$e time! is$nown to change.
derivative
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%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
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,"ten the $e- to relatingthe variables in this t-pe o"
problem is DRAWING APICTURE that shows the
geometric relationshipsbetween the variables.
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. #denti"- and LABELall the given in"o andwhat -ou are as$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.
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6et A be the Area o" a circle o" radius r. 7owis dA/dt related to dr/dt8
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6et 9 be the 9olume o" a cube o" side length .7ow is d9/dt related to d/dt8
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6et 9 be the 9olume o" a sphere o" radius r. 7ow isd9/dt related to dr/dt8
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V=
3 r2
h
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(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
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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
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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.
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Read 0.! 0?! 0;!
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