Differentiation (Normal, from First Principle)

Question 1

Differentiate y = ax^b?

Answer 1

y = abx^(b-1)

Question 2

What is differentiation?

Answer 2

The process that gives you a formula for the gradient function.

Question 3

How do you find the gradient???

Answer 3

Substitute the co-ordinates into the differentiated formula

Question 4

What is the normal?

Answer 4

A straight line perpendicular to the tangent where it touches the curve

Question 5

What is the formula to Differentiate from the First Principle?

Answer 5

h–>o f(x+h)–f(x) / h

Question 6

In Differentiation, what does x equal if the gradient is increasing?

Answer 6

x >= 0

Question 7

In Differentiation, what does x equal if the gradient is decreasing?

Answer 7

x =< 0

Question 8

What is the gradient at stationary points?

Answer 8

m=0

Question 9

How do you find the stationary points?

Answer 9

1. Differentiate
2. Solve to =0
3. Substitute

Question 10

How do you know if a stationary point is a maximum or a minimum?

Answer 10

y -> dy/dx -> d2y/dx2 -> substitute
positive = minimum
negative = maximum