Unit 3 Formulas

Question 1

EVT

(for closed intervals) - ABS MAX / MIN

Answer 1

1. Continuous
2. Critical Numbers (f’(x) , = 0 , = DNE)
3. Evaluate CN / Endpoints
4. Highest / Lowest

Question 2

Local Linear Approximation

Answer 2

y = f(x₀) + f’(x₀) (x-x₀)

Question 3

L’Hôpital’s Rule

Answer 3

lim x→a ( f’(x) / g’(x) )

dx of N , dx of D , limit of fraction

Question 4

Average Rate of Change

Answer 4

f(x) - f(x₀) / x - x₀

Question 5

Instantaneous Rate of Change

Answer 5

f’(x₀)

Question 6

Instantaneous Velocity

Answer 6

s’(t)

Question 7

Instantaneous Speed

Answer 7

|v(t)|

Question 8

Instantaneous Acceleration

Answer 8

s’‘(t)

Question 9

Rectilinear Motion

SAME SIGN
DIFFERENT SIGN

Answer 9

SAME SIGN - speeding up
DIFFERENT SIGN - slowing down