The following equation shows your retained information depending as a function of the hours of study. Say you wanted to find out at which point your ability to retain information (rate of retention) starts DIMINISHING. Find the number of hours of study at which this occurs. If this describes you, what is the best course of action after that amount of study? M(t) = -3t3 + 3t2 + 12t
The following equation shows your retained information depending as a function of the hours of study. Say you wanted to find out at which point your ability to retain information (rate of retention) starts DIMINISHING. Find the number of hours of study at which this occurs. If this describes you, what is the best course of action after that amount of study? M(t) = -3t3 + 3t2 + 12t
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hi yes i need help finding out how to do this problem and want to see what work and formulas it takes to complete this question, i attached a “tattoo” cheat sheet that has the derivative formulas that can be used to solve
![1. The following equation shows your retained information depending as a function of the
hours of study. Say you wanted to find out at which point your ability to retain
information (rate of retention) starts DIMINISHING. Find the number of hours of study
at which this occurs. If this describes you, what is the best course of action after that
amount of study?
M(t) = -3t3 + 3t2 + 12t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecdd705b-8f24-4267-a1a3-3a3290e71e31%2F64b5028a-2f3a-4526-91c2-b686c1ccdfaa%2Fbpf5uvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The following equation shows your retained information depending as a function of the
hours of study. Say you wanted to find out at which point your ability to retain
information (rate of retention) starts DIMINISHING. Find the number of hours of study
at which this occurs. If this describes you, what is the best course of action after that
amount of study?
M(t) = -3t3 + 3t2 + 12t
![*TATTOO"CHEAT SHEET - USE OFTEN!
youR
THE BASICS
derrv.
PX) MP
CO) MC
RX)
X - fcx)+y ly CAN BE +,Ø,-)
Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.})
integ
%3D
X *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION})
DERIVATIVES
PRODUCTS AND QUOTIENTS
y=x^ y'- nx^-
you"
u isA
FUNCTION,
%3D
U AND V
y=uv y'= u'v +uv
n-1
y'=nu" (u') X IS VAR.,
ARE
FUNCTIONS
y= e"
y'- u'e"
e AND ny= u y'= u'v -uv'
V
CONSTANTS
dautdin
y=Lnu y's 4
LOGS AND EXPONENTS
y=a" y'=a"u’ına ) WHERE u
IS A FUNC,
INTEGRALS
yoa" g =a*x' ina fais const,
+ X +K , n#-1
X IS VARVABLE
Fa*(1) Lna
ntl
+k, n+-1
in(e*) =x (SIMPLIFIED, NOT DERIVATIVE )
=X (SIMPUFIED, NOT DERIVATIVE)
+ e" +K
In(MN)= Ln M+ unN
in (A) - LnM -UnN
Lin(MP) =
y=lagax a =x
4- Ju'u"dx → inu tK n-
STEPS
WHERE M
EN ARE
FUNCTIONS.
(CONVERSIONS
NOT DERIVATIVES)
Pn M
WHICH INTEGRAL?
1) MAKE IT
2) FIND U; CREATE U'
3) WE HAVE
4) MAKE IT LOOK LIKE TEMPLATE
5) PERFORM INTEGRAL
PRETTY:
WE WANT.
CHANGE OF BASE:
y=loga x -LogX
= In x
loga
DEFINITE INTEGRALS
ALSO
Una
y=Sax'dx = afx*ax
y=S(ax^+bx") dx
Fa) = ffondx
JHondk = FO = F(b) - F(a)
"dx
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecdd705b-8f24-4267-a1a3-3a3290e71e31%2F64b5028a-2f3a-4526-91c2-b686c1ccdfaa%2Fieq28u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:*TATTOO"CHEAT SHEET - USE OFTEN!
youR
THE BASICS
derrv.
PX) MP
CO) MC
RX)
X - fcx)+y ly CAN BE +,Ø,-)
Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.})
integ
%3D
X *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION})
DERIVATIVES
PRODUCTS AND QUOTIENTS
y=x^ y'- nx^-
you"
u isA
FUNCTION,
%3D
U AND V
y=uv y'= u'v +uv
n-1
y'=nu" (u') X IS VAR.,
ARE
FUNCTIONS
y= e"
y'- u'e"
e AND ny= u y'= u'v -uv'
V
CONSTANTS
dautdin
y=Lnu y's 4
LOGS AND EXPONENTS
y=a" y'=a"u’ına ) WHERE u
IS A FUNC,
INTEGRALS
yoa" g =a*x' ina fais const,
+ X +K , n#-1
X IS VARVABLE
Fa*(1) Lna
ntl
+k, n+-1
in(e*) =x (SIMPLIFIED, NOT DERIVATIVE )
=X (SIMPUFIED, NOT DERIVATIVE)
+ e" +K
In(MN)= Ln M+ unN
in (A) - LnM -UnN
Lin(MP) =
y=lagax a =x
4- Ju'u"dx → inu tK n-
STEPS
WHERE M
EN ARE
FUNCTIONS.
(CONVERSIONS
NOT DERIVATIVES)
Pn M
WHICH INTEGRAL?
1) MAKE IT
2) FIND U; CREATE U'
3) WE HAVE
4) MAKE IT LOOK LIKE TEMPLATE
5) PERFORM INTEGRAL
PRETTY:
WE WANT.
CHANGE OF BASE:
y=loga x -LogX
= In x
loga
DEFINITE INTEGRALS
ALSO
Una
y=Sax'dx = afx*ax
y=S(ax^+bx") dx
Fa) = ffondx
JHondk = FO = F(b) - F(a)
"dx
%3D
%3D
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