Page 13-12
The interpretation of the variation table shown above is as follows: the
function F(X) increases for X in the interval (-
∞
, -1), reaching a maximum equal
to 36 at X = -1
.
Then, F(X) decreases until X
=
11/3, reaching a minimum of
–
400/27
.
After that F(X) increases until re
∞
.
Also, at X =
±∞
, F(X)=
±∞
.
Using derivatives to calculate extreme points
“Extreme points,” or extrema, is the general designation for maximum and
minimum values of a function in a given interval. Since the derivative of a
function at a given point represents the slope of a line tangent to the curve at
that point, then values of x for which f’(x) =0 represent points where the graph
of the function reaches a maximum or minimum. Furthermore, the value of
the second derivative of the function, f”(x), at those points determines whether
the point is a
relative or local maximum
[f”(x)<0] or
minimum
[f”(x)>0]. These
ideas are illustrated in the figure below.
In this figure we limit ourselves to determining extreme points of the function y
= f(x) in the x-interval [a,b]. Within this interval we find two points, x = x
m
and x = x
M
, where f’(x)=0. The point x = x
m
, where f”(x)>0, represents a local
minimum, while the point x = x
M
, where f”(x)<0, represents a local maximum.
From the graph of y = f(x) it follows that the absolute maximum in the interval
[a,b] occurs at x = a, while the absolute minimum occurs at x = b.
Содержание 49g+
Страница 1: ...hp 49g graphing calculator user s guide H Edition 4 HP part number F2228 90006 ...
Страница 197: ...Page 5 30 LIN LNCOLLECT POWEREXPAND SIMPLIFY ...
Страница 377: ...Page 11 55 Function KER Function MKISOM ...
Страница 457: ...Page 13 26 In the right hand side figure above we are using the line editor to see the series expansion in detail ...
Страница 775: ...Page 26 10 the location of the backup battery in the top compartment at the back of the calculator ...
Страница 838: ...Page L 5 ...