Solve f(x)=x^3-6x^2+15: Help Needed

[hectorubie]

Homework Statement

hey guys. please help me out i tried the problem but for some reason i feel like its wrong. thank you in advance.

Homework 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

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

 

[Dick]

Homework Statement

hey guys. please help me out i tried the problem but for some reason i feel like its wrong. thank you in advance.

Homework 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

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

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?

 

[hectorubie]

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?

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

 

[Ray Vickson]

Homework Statement

hey guys. please help me out i tried the problem but for some reason i feel like its wrong. thank you in advance.

Homework 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

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

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.

 

[hectorubie]

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.

i see where i did wrong there. thanks

 

[hectorubie]

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