derivative of x(n)?

What does value of derivative at point P tell you?

If gradient of tangent of m, what is gradient of normal?

if dy/dx is posotive at x=a, then is y increasing or decreasing?

if dy/dx is negative at x=a, then is y increasing or decreasing?

dy/dx = 0?

at local maximum, does dy/dx go from pos to neg or neg to pos?
local minimum?

second derivative posotive?
second derivative negative?

intergrate x(n)

What value does an area below the x-axis have?

Trapezium rule
h?
how to improve estimate?
cure below line segments?
curve above line segments?