Posted by **jerson** on Wednesday, November 12, 2008 at 11:12pm.

use the function G(x)=x^3-8x +1

b) identify and verify the y intercept of G

c) estimate the zeros of G to the nearest tenth

d) estimate the coordinates of the relative extrema of G to the nearest hundredth

e)in what intervals is G positive? Negative?

f) in what intervals is G increasing? Decreasing?

- trig -
**drwls**, Wednesday, November 12, 2008 at 11:27pm
This is not trigonmetry. You may have to do some plotting of G(x). We cannot do the graphing for you.

The relative extreme values can be obtained by setting the derivative equal to zero, giving

3 x^2 = 8

and solving for x

Please show your work if you need further assistance.

- trig -
**jerson**, Wednesday, November 12, 2008 at 11:36pm
this is trigonometry.. its the class i'm taking and my book is called, functions, statistics, and trigonometry. scott, foresman.

- trig -
**Damon**, Wednesday, November 12, 2008 at 11:39pm
when x = 0, G = 1

sketch a graph of this thing right off. Let y = G(x)

when x is big negative, y is big negative

when x is big positive, y is big positive

we know when x = 0, y = 1

since it is cubic, it may cross the x axis three times

when x = -1, y = 8

when x = +1, y = -6

That gives you a pretty good idea what it looks like

there is a zero left of -1, a zero between 0 and +1, and a zero right of +1

I will leave finding those zeros for you, guess and then guess again

Now You know there is an max around -1 and a min around +1

I would take the derivative to look for where, but you can guess and correct the guess

taking derivative and setting to zero

0 = 3 x^2 -8

x^2 = 8/3

x = +/- 1.63

so we have a max at x = -1.63 , you find y

we have a min at x=+1.63, you find y

Now you can easily make your graph more accurate to answer e and f

- trig -
**drwls**, Wednesday, November 12, 2008 at 11:50pm
Trigonometry concerns triangles. That subject may be part of your book, but is not the subject of your question. Your question is about functions.

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