Given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. help.

1. Dec 4, 2012

hectorubie

1. The problem statement, all variables and given/known data
hey guys. please help me out i tried the problem but for some reason i feel like its wrong. thank you in advance.

2. Relevant equations
given f(x)=x^3-6x^2+15
a)find the intervals of inc/dec
b)find the local max/min if any
c)find intervals of concavity
d)find the inflection points if any
e)use the information to sketch the graph

3. The attempt at a solution

f'(x)=3x^2-32x
=x(3x-32)
x=0 x=32/3 (critical points)

from -infinity to 0 the function is positive
from 0 to the function is negative
from 32/3 to infinity the function is positive

f(0) = 15 (0,15) = local min
f(32/5) = 35.7 = local max

f''(x)=6x-32
=6x-32=0
=16/3

from -infinity to 16/3 the function is concave down
from 16/3 to infinity the function is concave up

point of inflection (16/3, 15)

cant show the graph here

2. Dec 4, 2012

Dick

Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

Your derivative is wrong. Try and fix that and try again. And whether the derivative is positive or negative tells you whether the function is increasing or decreasing, yes?

Last edited: Dec 4, 2012
3. Dec 4, 2012

hectorubie

Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

the first derivative is 3x^2-32x
i factored it to x(3x-32). is that wrong?

4. Dec 4, 2012

Ray Vickson

Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

The function f(x) =x^3-6x^2+15 is NOT positive on (-∞,0): when x is large and negative the x^3 term is swamps all the others and is < 0, so f(x) < 0.

5. Dec 4, 2012

hectorubie

Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

i see where i did wrong there. thanks

6. Dec 4, 2012

hectorubie

Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

i see where you say the deriv was wrong...
the derive is 3x^2-12x sorry i didnt notice that i did that

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