文档介绍：CALCULUS
A DERIVATIVE FUNCTION
The derivative function or simply the derivative is defined as
==
Find the derivative function
Find ,
Find the average rate of change ,
Find the limit .
Geometric significance
Consider a general function y=f(x), a fixed point A(a,f(a)) and a variable point B(x,f(x)). The slope of chord AB=.
Now as BA, xa and the slope of chord ABslope of tangent at A.
So, is .
Thus, we can know the derivative at x=a is the slope of the tangent at x=a.
Rules
C(a constant)
0
The chain rule
If where then .
,
6. Inverse function, Parametric function and Implicit function
Inverse function:, ,
., ,
Parametric function:,
., ,→,
Implicit function: , .
, , t
High derivative
y=sinx ,
B APPLICATIONS OF DIFFERENTIAL CALCULUS
Monotonicity
If S is an interval of real numbers and f(x) is defined for all x in S, then:
f(x) is increasing on S for all x in S, and
f(x) is decreasing on S for all x in S.
Find the monotone interval
Find domain of the function,
Find , and x which make ,
Draw sign diagram, find the monotone interval.
Maxima/Minima, Horizontal inflection, Stationary point
C INTEGRAL
The idea of definite in