English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

sketch graph
find max/min
concavity
inflection points

2006-11-02 15:53:33 · 5 answers · asked by rico7973 1 in Science & Mathematics Mathematics

5 answers

y' = 3x^2 + 12x + 9 = 3(x^2 + 4x + 3) = 3(x+1)(x+3), so critical numbers are x = -1, -3

y'' = 3(2x+4) = 6(x+2), so inflection point is at x = -2.

at x = -1, y'' > 0, so x = -1 is a min
at x = -3, y'' < 0, so x = -3 is a max

y is increasing for x < -3 and x > -1, and decreasing otherwise
y is concave up for x > -2, and concave down for x < -2

2006-11-02 16:04:52 · answer #1 · answered by James L 5 · 1 0

y' = 3x^2 + 12x + 9 = 3(x^2 + 4x + 3) = 3(x+1)(x+3),
so critical points are x = -1, -3
y'' = 3(2x+4) = 6(x+2), so inflection the point is x = -2.
at x = -1, y'' > 0, so x = -1 is a min
at x = -3, y'' < 0, so x = -3 is a max
y is increasing for x < -3 and x > -1, and decreasing otherwise
y is concave up for x > -2, and concave down for x < -2
s

2006-11-03 14:52:26 · answer #2 · answered by Anonymous · 0 1

Compute its derivative to find the answers.
y=x^3+6x^2+9x,
so y'=3x^2+12x^2+9, and y''=6x+12.
let y'=0, we can find x=-1 or x=-3.
when x=-1,y''>0,white y''<0 when x=-3.
So, you can make analysis based on these two points.

2006-11-02 16:24:13 · answer #3 · answered by Anonymous · 0 0

don't know how to sketch it on the computer..
(-3,0) touches graph and comes back down parabola opens down
(-1,4)mini parabola opens up
(0,0) goes through origin
skims up along the y-axis
Range =-infinity to infinity
kind of makes a shape like an "N" but not quite.

2006-11-02 16:07:06 · answer #4 · answered by Dawn J 4 · 0 0

Yeah it would make experience in case you needed help with only one difficulty to comprehend the basics, yet you % people to do all your homework. attempt no longer dozing by type next time.

2016-11-27 00:41:53 · answer #5 · answered by Anonymous · 0 0

fedest.com, questions and answers