Question

find all critical points of the fxn

Fx=x^3-9/2x^2-54x+2

Answer 1

did you mean
f(x)=(x^3-9)/(2x^2-54x+2)
or is it
f(x)=x^3-9/2x^2-54x+2?

Answer 2

Whatever the function, the first step is to find the derivative

Answer 3

\[f(x)=x ^{3}-\frac{ 9 }{ 2 }x ^{2}-54x\]

Answer 4

oh that is much easr that what I have imagined

Answer 5

do you know power rule?

Answer 6

\[(x^n)' = n \cdot x^{n-1}\]

Answer 7

x^n=nx^(n-1)

Answer 8

yep apply that to each term

Answer 9

\[(x^3)'=?\]

Answer 10

3x^2

Answer 11

\[(-\frac{9}{2}x^{2})' =\frac{-9}{2}(x^2)'=?\]

Answer 12

-9x???

Answer 13

yep

Answer 14

and finally
\[(-54x)'=?\]

Answer 15

-54

Answer 16

right

Answer 17

so put the three terms together and you are done

Answer 18

\[f(x)=x^3-\frac{9}{2}x^2-54x \\ f'(x)=(x^3)'-\frac{9}{2}(x^2)'-54(x)' \\ f'(x)=3x^2-\frac{9}{2}(2x)-54(1) \\ f'(x)=3x^2-9x-54\]

Answer 19

well done with the derivative

Answer 20

you still need to find the critial numbers :p

Answer 21

you can do that by replacing f'(x) with 0

Answer 22

ok so whats the next move?

Answer 23

\[0=3x^2-9x-54\]
and solve

Answer 24

solve how exactly?

Answer 25

it is a quadratic equation...
you can try factoring or using the quadratic formula...

Answer 26

\[3(x ^{2}-3x-18)\]

Answer 27

ok do you know how to factor x^2-3x-18?

Answer 28

not exactly. there arent any common terms

Answer 29

do you know how to find two numbers that when you multiply them you get -18 but add them and get -3?

Answer 30

-6 and 3

Answer 31

so the factored form of x^2-3x-18 is (x-6)(x+3)

Answer 32

oh my goodness sorry i should have realized that my brain is so fried so it would be 6 and 3?

Answer 33

6 and -3

Answer 34

-3

Answer 35

thank you so much

Answer 36

np