Week 8 Calculus I Outline of Notes

by S. Gramlich

(updated 10/30/06)

I) 3.7 Higher Derivatives (1st, 2nd, 3rd derivatives)

Notation

s = position

s'= velocity

s''= acceleration

p. 241, #26

II) 3.8 Derivative of Log & Ln Formulas

p. 249, #4,6

Logarithmic Differentiation

1) take Ln of both sides

2) differentiate

3) solve for y'

4) substitute for y

p. 249, #40

III) 3.10 Related Rate Applications= find unknown rate of change

1) use Geometry formulas from inner flap of text

2) differentiate wrt time

3) substitute given quantities

4) solve algebraically for unknown rate of change

p. 260, #8

IV) 3.11 Linear Approximation: f(x) ~ f(a) +f'(a)*(x-a)

p. 267, #6

3.11 Differential: dy= f'(x)*dx

p. 268, #26