Question

consider the function g(x) = x^3 - (5/2)x^2-2x+1. List any points of inflection. Please show work

Answer 1

To find the inflection points you have to derive the following function twice. After that, take 2 conditions for f''(x).

(a) f''(x) = 0
(b) f''(x) DNE

after that take f''(x) = 0 and find the zeros of the function, those zeros will be your inflection numbers, then substitute them in the function to get their y :) and your done ^_^

Give it a try :)

Answer 2

what's DNE

Answer 3

Doesn't exist, and you can use that case if and only if we have x in the denominator :)

Answer 4

so in your case, you have a function that is considered a polynomial which means the range and domain is R, so you can factor out f''(x) and find the zeros ^_^

Answer 5

clearer? :)

Answer 6

i would factor out x out of the original function but what about the 1

Answer 7

lol, no, to find the inflection points you have to take 2 conditions, like I have said before, but since for x, x exists , you must take the zeros of f''(x) and not f(x) :)

Answer 8

oh you said factor out the second derivative. sry for the misunderstanding

Answer 9

lol, no worries ^_^ yeah, the second derivative = f''(x) :) give it a try now.

Answer 10

ok

Answer 11

good luck :)

Answer 12

thx

Answer 13

np ^_^

Answer 14

the 2nd deriv only gives me one number when = to zero

Answer 15

so that's your inflection number :), I didn't calculate it yet, but if that's what you got, then that's the inflection number ^_^

Answer 16

so i sub that in for all the Xs

Answer 17

yes to get the y, and then you'll have an inflection point (x,y) ^_^

Answer 18

if i substitute it in it will only give me one #, how is that a point? sry if i'm not understanding correctly

Answer 19

no it's alright. Calc dear, when you found the inflection number by getting the zeros, then you have found point x. When you substitute x in the original function, you'll get point y , f(x) = y. Solve for y :)

Answer 20

Did you understand it now? ^_^

Answer 21

gotchya

Answer 22

awesome :)

Answer 23

thx alot that helped

Answer 24

np ^_^ wish you all the best

Answer 25

thnk u

Answer 26

:) np