- #1
hectorubie
- 4
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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