null
US
Sign In
Sign Up for Free
Sign Up
We have detected that Javascript is not enabled in your browser. The dynamic nature of our site means that Javascript must be enabled to function properly. Please read our
terms and conditions
for more information.
Next up
Copy and Edit
You need to log in to complete this action!
Register for Free
1769425
Calculus I
Description
Mind Map on Calculus I, created by GraceEChem on 08/12/2014.
No tags specified
math 111 - university calculus i
calculus 1
Mind Map by
GraceEChem
, updated more than 1 year ago
More
Less
Created by
GraceEChem
about 9 years ago
604
19
0
Resource summary
Calculus I
Limits
Infinite limits
Divide top and bottom by biggest power
1/x^n = 0
Finite limits
Continuous, plug in constant
0/0 is your answer?
Factor and Simplify
Derivatives
Product Rule
(fg)' = f'g+g'f
Quotient Rule
(f/g)' = (f'g - g'f) / g^2
Power Rule for Functions
(f^n)' = nf^(n-1)f'
Chain Rule
dy/dx = (dy/du)(du/dx)
for y=y(u) and u=u(x)
[f(g(x)]' = f'(g(x))g'(x)
Finding 2nd Derivative
just take the derivative of the derivative
f(x) = e^x, f'(x) = e^x
f(x) = ln x, f'(x) =1/x
g(x) = loga(x), g'(x) = (1/ln a)(1/x)
f'(x) = ln(a)a^x
Chain Rule and Logs
g(x) = ln(f(x))
f'(x)/f(x)
ln(x) + 1/x (x')
Marginal Analysis/Linear Approximation
f(x+delta x) ~= f(x) + delta x(f'(x))
or Marginal Cost = C'(x)
Implicit Differentiation
Treat x as x and y as f(x), give derivative of y w/respect to x
Differentiate both sides w/respect to x with y as f(x)
Chain rule, differentiating terms with y
Solve for dy/dx in terms of x and y
Increasing/Decreasing Functions
Use 1st Derivative
Test points @ f'(x) = 0
Plug test points into f'(x)
And where f'(x) does not exist
CRITICAL POINTS!
Concavity
Use f''(x)
Test points @ f''(x) = 0
And where f''(x) does not exist
Inflection point where concavity changes
Positive/Negative
Test points on f(x)
Optimization
x = c is critical point if f'(c) = 0
x = c relative min/max if f'(c) changes sign
x = c abolute min/max
Closed Interval
find where f'(x)=0
plug those points into f(x)
compare against interval points for absolute max/min
Open Interval
find one critical point, where f'(x)=0
this shows concavity
Exponents
Compound interest
Yearly
P(t) = P(1+r)^t
Monthly
P(t) = P(1+r/12)^12t
Continuously
P(t) = Pe^rt
Show full summary
Hide full summary
Want to create your own
Mind Maps
for
free
with GoConqr?
Learn more
.
Similar
Limits AP Calculus
lakelife62
Calculus & Integral 1 - Known limits
Bassam Mansour
Basic Derivative Rules
Bill Andersen
Calculus
natz994
Calculus II Improper Integrals
Anthony Campos
Integration Techniques
Rob Grondahl
Techniques of Integration
hamidymuhammad
STRATEGY OF INTEGRATION
intan_syahirah97
Derivadas
Roxy Hughes
Series Strategy
Rob Grondahl
Mathematicalproving
Sharifah Huda
Browse Library