Increment. The basic property of a linear function
increment of x,y
The difference between the final
and initial values of the independent variable x on transition from the initial value
to the final value is called the increment of x,
equal to
The difference between the final and initial values of the
function y = f(x)
is called the corresponding increment
of the function:
These
increments are often denoted by:
It must be pointed out that the symbol
x has to be regarded as a single entity in denoting the increment of x. We
shall consider the case of a linear function, when
Subtracting
term by term, we have:
This
equality shows that the linear function y = ax -b has the property
that the increment of the function (y2 - y1)
is proportional to
the increment of the independent variable
(x2- x1), the coefficient of
proportionality being equal
to a, i.e. to
the slope of
the graph of the function. Turning
to the graph itself (Fig.
8), corresponding to the increment of
the independent variable we
have the segment X1P =
x = x2 - x1 and
corresponding to
the increment of the function, PM2 =
y = y2-y1 ; and formula(4) follows at once from considering the triangle M1pM2.
the source:
A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.
By: Fady tarek
0 comments:
Post a Comment