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?
drwls
answered
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.
jerson
answered
Damon
answered
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
drwls
answered