Differntiaitom

Question 1

How to see nature of stationary point

Answer 1

Second errivwitve shows the rate of change of gradient, so if it’s negative the gradient is getting negative

So if the second is negative, that means your thing is going from positive to negative , and so maximum

If second is positive then neagtive becomes postiive so minimum

If it’s 0 you can’t tell, must use standard check gradient on weither side of the thing check
- this becomes a stationary point of INFLECTION

Question 2

How to find non stationary points of inflection?

Answer 2

All points of inflection have their second derrivstive as 0, but not all 0 second derrivstive are points of inflection
- differntiate twice and see where second is zero
- now test these left and right if SECOND DERRIVSITVE , and if that shows a change in concavity then it is A POINT IF INFKECTION

Question 3

Remember chain rule for rates, how to make required equation ?

Answer 3

Write what you want , what you have and what you need to cancel like fractions

Remember dx/dy is the reverse

Question 4

Turnign points nature when quotient rule is used and itshard ! What to do?

Answer 4

Jus use standard test left right feature because differentiating again would be quite hard