What is a point of inflection?
A point o inflection is where concavity of graph changes
Where d2y/dx2 = 0
What does it mean when d2y/dx2 > 0 ?
It is concave upwards
What does it mean when d2y/dx2 < 0 ?
It is concave downwards
What does it mean when d2y/dx2 = w ?
When x increases by 1, dy/dx increases by ‘w’
How do you prove a point of inflection?
A point o inflection is proved by subbing into dy/dx of values either side of the point to prove a change
What is the chain rule?
dy/dx = dy/du x du/dx
Where for function y = (2x+5)3, u = 2x+5
How can the chain rule be used to solve problems to do with connected rates of change?
The derivative can be split up into 2 separate ones:
dV/dt = dV/dh x dh/dt
What is the product rule?
If y = uv:
dy/dx = u(dv/dx) + v(du/dx)
Where function y = 20x(x-1)6
u = 20x and v = (x-1)6
What is the quotient rule?
If y = u/v:
dy/dx = (v(du/dx) - u(dv/dx))/v2
Where function y = x2 / 1+2x3
u = x2 and v = 1+2x3
How do you find the derivative of a function with ‘x’ as the subject?
d𝑥/d𝑦= 1/(d𝑦/d𝑥)
