in.nb

$RowBox[{Sketch, , the, , graph, , of, , Cell[y = x^3<br />], Cell[<br />]}]$

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$Plot[x^3, {x, -6, 6}]$

[Graphics:HTMLFiles/in_5.gif]

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$Plot[10 * x^3, {x, -6, 6}]$

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$Plot[-10 * x^3, {x, -6, 6}]$

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$Plot[x^3 - 4x, {x, -4, 4}]$

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$Plot[x^3 - 4x - 6, {x, -4, 4}]$

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$Plot[(1/4) * x^3, {x, -4, 4}] $

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$Plot[x^3 - x^2 - 3x + 2, {x, -4, 4}]$

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Finding Intercepts 1. To find x - intercepts, let y be zero and solve the equatoion for x . &# ... . To find y - intercepts, let x be zero and solve the equation for y . 

a . y = x^3 - 4x Solution a . Let y = 0. Then 0 = x^3 - 4x = x (x^2 - ... Then y = (0)^3 - 4 (0) = 0 y - intercepts : (0.)

Let dy/dx = 0, then find (x, y).

y = x^3 - 4x

dy/dx = 3x^2 - 4

0 = 3x^2 - 4

x = - 1.06, x = 1.06 y = 3.05, x = -3.05

Use intercepts to grahp. Find the intercepts, then put the intercepts in the xy phase plane. connect all points.

point: (0, 0), (2, 0), (-2, 0), (1.06, -3.05), (-1.06, 3.05)

Find the intercepts and let dy/dx = 0, then find the (x, y). Grahp the equation.

1. y = x^3 - 5x^2 - x + 5

2. y = 27x^3 - 18x^2 -48x + 32

The solution

Notebook

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Created by Mathematica (April 20, 2004)