Math 115 Lab #4
M. Flashman
I. Entering Functions.
II. Increasing and decreasing functions.
III. Functions and
Slopes of Secant Lines.
 Tools for Winplot used in this lab:
 Equation menu
 User Function
 name box
 name (x) = box
 enter
 Point (x,y)
 Segment (x,y)
 One Function
Menu
 Secant
check box and slope.
 Anim Menu
I.Entering
Functions. Demonstration.
 Equation menu
 name (x) = 2x^3 
5x^2
 x + 4
 Explicit
 Point (x,y)
 x=0 y=g(0) ;
 x=a y = g(a)
 Use animation slider for A...
 Segment (x,y)
 x1 = 0 y1 = g(0)
 x2 = a y2 = g(a)
 Use animation slider for A...
II. Increasing and decreasing functions.*
Example:
Consider the function f
where
f(x) = 2x^{3}  5x^{2}
 x + 4 with x in the domain [5, 5].
 Using Winplot find the local extreme points and values
for the function.
 ANS:
 local min: (x,y) =
(1.76129406047167,2.34445731940242)
 local max::(x,y) =
(0.09462739380500,4.04816102310612)
 Determine approximately the interval(s) where
the function is increasing .....decreasing.
 ANS:
 The function is increasing for the approximate
intervals [5,0.0946] and [1.7613, 5].
 The function is decreasing for the approximate
interval [0.09463, 1.76129]
Record your answers for
the next work and submit them on Moodle by Wednesday, Feb. 17
For each of the following functions determine
approximately the interval(s) where the function is increasing on
the domain [5, 5].
 f(x) = x^{3} + 3x^{2}
 4
 f(x) = 2x^{3}  3x^{2} + 4
III.
Functions and Slopes of Secant Lines.
Basic Terminology:
If a line passes through a curve at two distinct points,
the line is described as a secant
(cutting) line.
We will investigate secant lines determined by two points on the graph
of
functions. In particular, your task will be to find the slopes of these
lines,
using Winplot.
Example: Consider the function f where
f(x) =5x^{2}
 3x + 4.
 Use Winplot's slider
to look for the values of f(1) and f(3).
 Use these values to
find the slope of the secant line passing through the function's graph
at the points (1, f (1)) and (3,f(3)).
 Verify this result on
Winplot using the secants feature of the slider
as follows:
 Position
your slider with "x =" 1. <enter>
 Check of the box labelled "secants at base
point."
 In the "x = " box enter 3. <enter>
 Read the result on the slider from "slope:
"
 Use the slider to find the slopes of secant
lines passing through the point (1, f (1))
and each of the following points:

(2,f(2));
(1.5,f(1.5));
 (1,f(1)); (0,f(0)); (0.5,f(0.5))
Record your answers for
the next work and submit them on Moodle by Wednesday, Feb. 17
For
f(x) = x^{3} + 3x^{2}
 4
find the slopes of secant lines passing through the point (1, f (1))
and each of the following points:
 (1, f (1)) and
(2,f(2));
 (1, f (1)) and
(1.1,f(1.1));
 (1, f (1))
and (0,f(0));
 (1, f (1))
and (0.9,f(0.9))
End of Lab 4