Final Exam Flashcards
Limits 10-1
The Limit as X approaches a number
lim f(2+h) - f(2)/h
The Derivative 10-4
f’(x) = lim h->0 [f(x+h) - f(x)]/h
Marginal Analysis 10-7
Revenue, Cost, Profit
Cost
Total Cost: C(x)
Marginal Cost: C’(x)
Revenue
Revenue: (# of items made)(price per item)
Total Revenue: R(x)
Marginal Revenue: R’(x)
Profit
Total Profit: P(x) = R(x) - C(x)
Marginal Profit: P’(x)= R’(x) - C’(x)
e and Interest 11-1
A=Pe^rt
Derivative with e 11-2
Derivative of e^x = e^x
Derivative of lnx = 1/x
Product and Quotient Rule 11-3
Product Rule
y = f(x) = F(x)S(x)
f’(x) = F(x)S’(x) + F’(x)S(x)
Quotient Rule
y = f(x) = T(x)/B(x)
f’(x) = [B(x)T’(x) - T(x)B’(x)]/[B(x)]^2
Chain Rule 11-4
Derivative of f(x)^n = n[f(x)]^n-1 x f’(x)
Derivative of ln[f(x)] = 1/f(x) x f’(x)
Derivative of e^f(x) = e^f(x) x f’(x)
Elasticity of Demand 11-7
Elasticity of Demand Function
E(p) = -[f’(p)/f(p)] x p
Relative Rate of Change
f(x) = f’(x)/f(x)
Percentage Rate of Change
100 x f’(x)/f(x)
Inelastic: >1
Elastic: <1
Unit Elasticity: =1
First Derivative 12-1
Use to find Critical Values on a Curve Sketch
Set f’(x) = 0
x=?
Find where it’s Increasing and Decreasing as well as Local Maximum and Local Minimum
Second Derivative 12-2
Use to find Concavity in Curve Sketch
Concave Upward or Downward
Find the Inflection Points
Optimization 12-6
Maximize Area
Find function
Take Derivative
Set = 0
Solve for x
Anti-Derivative and Integrals 13-1
The integral symbol: S
1: S x^n dx = (x^n+1)/ n+1 + C
n can not = -1
2: S e^x dx = e^x + C
3: S 1/x dx = ln |x| + C
x can not = 0
