Question

point of inflection

Answer 1

I have the second derivative (ie that is all I am given)
Can I find the relative maximum and the point of inflection with only the second derivative?

Answer 2

x^3(e^-x)(sinx) + 1/2 for 1<x<6

Answer 3

I know that the function concaves up , then down, then up again because I am looking at the graph

Answer 4

local max : second derivative < 0
inflection : second derivative = 0

Answer 5

x^3(e^-x)(sinx) + 1/2

this is second derivative, right ?

Answer 6

yes

Answer 7

for inflection points, we set it equal to 0 and solve x

Answer 8

second derivative is between 3.5 and 5.47

Answer 9

let me regraph this, this is suppose to be a graphing calculator problem

Answer 10

we can find the inflection points easily
but im not so sure how we cna get the max points.. @Kainui help

Answer 11

Using my graphing calculator, I found 3.5406074 and 5.470288 as my zeros

Answer 12

yes, 3.5 and 5.47 are the points of inflection

Answer 13

http://www.wolframalpha.com/input/?i=x%5E3*%28e%5E%28-x%29%29*%28sinx%29+%2B+1%2F2+%3D+0%2C+1%3Cx%3C6

Answer 14

they are both listed as points of inflections for choices. Those are the points of inflections for the original function. What would the point of infection be for the 1st derivative of the function?

Answer 15

the two questions I am stuck on are:
f prime has a relative maximum at x=?
f prime has a point of inflection at x=?

Answer 16

ahh these we can answer

Answer 17

f' will have a max/min when f''=0, right ?

Answer 18

yes

Answer 19

and, f'' = 0 when x = 3.5 and 5.47

Answer 20

yes

Answer 21

is it 3.5

Answer 22

And at relative max, the slope of tangent lines decrease.
so yes, 3.5 is the relative max !

Answer 23

cuz, around 3.5, f'' is decreasing => f''' is negative => relative max for f'

Answer 24

Can I use the + and - for 2 things? I thought the second derivative test tells us concavity. I thought the only thing I could use the graph for is to tell where the function concaves up and concaves down

Answer 25

yup !

f'' is decreasing => f' graph looks like below :