TOPIC 12: APPLICATIONS OF DIFFERENTIATION

Question 1

How to draw dy/dx graph?

Answer 1

1. Stationary points: y=0
2. Positive gradient: Above x-axis
3. Negative gradient: Below x-axis
4. Increasing gradient: Increasing graph
5. Decreasing gradient: Decreasing graph
6. Point of inflexion: Stationary point

Question 2

First Derivative Test

Answer 2

y ( x+ / x / x-)
Explanation
Slope
Sign
Min / Max / Point of Inflexion

Question 3

Second Derivative Test

Answer 3

d2y/dx2 > 0: Minimum point
d2y/dx2 < 0: Maximum point
d2y/dx2 = 0: No conclusion

Question 4

Relation between gradient of tangent and normal

Answer 4

m₁m₂ = -1

Question 5

Equation of tangent and normal

Answer 5

(y - y₁) = m₁ (x - x₁)
(y - y₁_ = -1/m₁ (x - x₁)

Question 6

General Steps for connected rate of change

Answer 6

1. Find equation relating x and y (ONLY 1 variable)
2. Implicit differentiation with respect to parameter t
3. Sub value of specific point