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MAPLE Assignment Solutions: Function Behavior and Extrema, Assignments of Analytical Geometry and Calculus

George Mason University (GMU)Analytical Geometry and Calculus

The solutions to maple assignment problems focusing on calculating functions, identifying local extrema, and determining absolute maxima and minima.

Typology: Assignments

Pre 2010

Uploaded on 02/10/2009

koofers-user-6i1-1
koofers-user-6i1-1 🇺🇸

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>
MAPLE Assignment #3 -- SOLUTIONS
#1(a)
> f:= x/(25 Kx2)01
31
f:= x/(25Kx2)(1/3)
> g:= x/D(f)(x)
g:= x/(D(f))(x)
> eval (g(x))
K2
3 x
(25Kx2)(2/3)
> L:= x/f(3)
C g(3)$(xK3)
L:= x/f(3) Cg(3) (xK3)
> eval (L(x))
16 (1/3) K1
8 16 (1/3) (xK3)
>
#1(b)
> plot ([f(x), L(x)],x=1..4)
pf3
pf4
pf5

Partial preview of the text

Download MAPLE Assignment Solutions: Function Behavior and Extrema and more Assignments Analytical Geometry and Calculus in PDF only on Docsity!

MAPLE Assignment #3 -- SOLUTIONS

#1(a)

> f := x / ( 25 K x^2 )

f := x / ( 25 K x^2 )

( 1 / 3 )

> g^ :=^ x^ /^ D (^ f^ ) (^ x^ )

g := x / ( D( f ) ) ( x )

> eval ( g ( x ) )

K

x ( 25 K x^2 )

( 2 / 3 )

> L := x / f ( 3 ) C g ( 3 ) $ ( x K 3 )

L := x / f ( 3 ) C g ( 3 ) ( x K 3 )

> eval^ (^ L^ (^ x^ ) )

16 ( 1 / 3 )^ K

16 ( 1 / 3 )^ ( x K 3 )

>

#1(b)

> plot ( [ f ( x ) , L ( x ) ] , x = 1 ..4 )

#1(c)

> plot ( | f^ (^ x^ )^ K^ L^ (^ x^ ) |,^ x^ = 1 .. )

Local maxima appear to be located approximately at x=-1,

.6, and local minima at x=-.25 and x=2.5.

#2(b)

> g := x / D ( f ) ( x )

g := x / ( D( f ) ) ( x )

> eval ( g ( x ) )

20 x^4 K 36 x^3 K 48 x^2 C 24 x C 12

> fsolve^ (^ g^ (^ x^ ) = 0 )

K1.051552693, K.3393516909, 0.6658980048, 2.

>

Local maximum values:

> f^ (^ K1.051552693 )

> f ( 0.6658980048 )

>

Local minimum values:

> f ( K.3393516909 )

K

> f^ ( 2.525006379 )

K

>

For absolute max and min values also include endpoints.

> f ( K2 )