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## 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