Question

Give the value of x where F(x) = X^3-33/2X+84x-2 what is the local minimum?

Answer 1

how do i find the roots of this?

Answer 2

you mean the roots of F or the roots of \(F'\)?

Answer 3

oh yes

Answer 4

if you are looking for a local max or mean you need the roots of \(F'\) ok we need to find \(F'\) first

Answer 5

i got 3X^2 -66/2x+84=0

Answer 6

i am not to good with finding roots in general so many different methods and coeffecients mess me up.Can you give me general way that will work for all types of polynomials?

Answer 7

no and it looks like your derivative is not right. here is what wolfram told me
http://www.wolframalpha.com/input/?i=%28x^3-33%29%2F%282x%2B84x-2%29

Answer 8

you have to use the quotient rule when taking the derivative.
it looks like you took the derivative top and bottom separately, and that doesn't work

Answer 9

im sorry its 33/2x ^2 seperate from rest

Answer 10

\[x^3-\frac{33}{2x}+84x-2 \]

Answer 11

made mistakae here is the correct f(x)= x^3-33/2x^2 +84x-2

Answer 12

did i get it right?

Answer 13

i fixed it

Answer 14

do you see it?

Answer 15

yeah it is this i think
\[x^3-\frac{33}{2x^2}+84x-2\]

Answer 16

x^2 comes after 33/2

Answer 17

oooooooooooooooooooooh

Answer 18

lol im sorry for the trouble

Answer 19

\[x^3-\frac{33}{2}x^2+84x-2\] in that case we are in good shape
no trouble
take the derivative
get a polynomial of degree 2
if it does not factor, use the quadratic formula!

Answer 20

\[f'(x)=3x^2-33x+84\] set the equal zero and solve

Answer 21

is quadratic formula practical on a test?

Answer 22

bet this one factors
\[f'(x)=3(x^2-11x+28)\]

Answer 23

maybe we get lucky
\[x^2-11x+28=0\]
\[(x-7)(x-4)=0\] etc

Answer 24

nice!

Answer 25

so we get \(x=4, x=7\) as the critical points, obviously 4 will give a local max and 7 a local min

Answer 26

so with those points u plugged back into f'(x) or F(x)?

Answer 27

oh be careful here

Answer 28

if you plug them back in to \(f'\) you will get 0 because that is how we found them to begin with
if you want the y values plug them in to \(f\) not \(f'\)

Answer 29

thanks

Answer 30

yw