MAPLE demo 2-13-07
Look at tangent and secant lines.
Example f(x)=x^3+5/x^2 at x_0=2.
> f:= x/x3C5
x2
f:= x/x3C5
x2
> plot (f(x), x=.5 ..6 )
>
Define the difference quotient for f(x) at x=2.
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Calculating Tangent and Secant Lines of a Function using Maple, Assignments of Analytical Geometry and Calculus
This document demonstrates how to calculate the tangent and secant lines of a function f(x) = x^3 + 5/x^2 at x_0 = 2 using maple. It includes the definition of the difference quotient, the calculation of the limit as h approaches 0, and the plotting of the tangent line and secant lines.
Typology: Assignments
Pre 2010
1 / 15
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MAPLE demo 2-13-
Look at tangent and secant lines.
Example f(x)=x^3+5/x^2 at x_0=2.
> f^ :=^ x^ /^ x^3 C^
x^2
f := x/x^3 C
x^2
> plot^ (^ f^ (^ x^ ) ,^ x^ =.5 ..6 )
>
Define the difference quotient for f(x) at x=2.
> q := h /
( f ( 2 C h ) K f ( 2 ) ) h
q := h/
f ( 2 C h ) K f ( 2 ) h
> q ( 3. )
> s1 := x / f ( 2 ) C q ( 3. ) $ ( xK 2 )
s1 := x/f ( 2 ) C q ( 3. ) ( x K 2 )
> plot ( [ f ( x ) , s1 ( x ) ] , x =.5 ..6 )
> q ( .1 )
> limit ( q ( h ) , h = 0 )
43 4
>
Plot the tangent line.
> t := x / f ( 2 ) C 0
$ ( x K 2 )
t := x/f ( 2 ) C
x K
> plot ( [ f ( x ) , t ( x ) ] , x =.5 ..3 )
>
Define some graphs of secant lines.
> s2 := x / f ( 2 ) C q ( .5 ) $ ( xK 2 )
s2 := x/f ( 2 ) C q ( 0.5 ) ( x K 2 )
> s3 := x / f ( 2 ) C q ( .2 ) $ ( xK2 )
s3 := x/f ( 2 ) C q ( 0.2 ) ( x K 2 )
> s4 := x / f ( 2 ) C q ( .05 ) $ ( xK2 )
s4 := x/f ( 2 ) C q ( 0.05 ) ( x K 2 )
> plot ( [ f ( x ) , s2 ( x ) , s3 ( x ) , s4 ( x ) , t ( x ) ] , x = 1.5 ..3 )
>
Look at tangent line as best linear approximation.
> plot ( f ( x ) , x = 1.75 ..2.25 )
> plot ( f ( x ) , x = 1.9 ..2.1 )
> plot ( [ f ( x ) , t ( x ) ] , x = 1 ..3 )
> plot ( [ f ( x ) , t ( x ) ] , x = 1.75 ..2.25 )
> plot ( [ f ( x ) , t ( x ) ] , x = 1.95 ..2.05 )
> plot ( [ f ( x ) , t ( x ) ] , x = 1.99 ..2.01 )