Question

i need help finding the critical numers of f(x)=x^3+3x^2-24x

Answer 1

Use dy/dx = 0

Answer 2

First you have to factor out the x

Answer 3

x(x^2+3x-24) than you factor the parenthesis

Answer 4

i dont think the inside is factorable, is it?

Answer 5

No it isn't you have to use quadratic formula

Answer 6

do you have to give approximate or exact values

Answer 7

oh man even the quadratic formula doesnt work o.O? it just says find critical values of the function

Answer 8

Quadratic formula does work. approximate answer (using calculator) is -6.623 and3.623

Answer 9

but exact answers are more involved

Answer 10

my book says the answers are -4,2... i think my book is wrong :(

Answer 11

are you doing calculus

Answer 12

YES

Answer 13

if you are doing derivative tests then you will have to take the derivative of this

Answer 14

and then solve for 0

Answer 15

Derivative is 3x^2+6x-24. Set that equal to zero and solve. Those x values will be the critical points.

Answer 16

The derivative of your function is : 3x^2+6x-24, now we can factor out a 3

Answer 17

3(x^2+2x-8)

Answer 18

now that inside can certainly be factored

Answer 19

3(x-2)(x+4)

Answer 20

Now set each term to zero, and you should get two critical points

Answer 21

and the answer is 2 and -4

Answer 22

wonderful ! i get it now thanks guys!