## bri 5 years ago the function f(x) = e^x - x^3 has how many critical points?

1. anonymous

What is critical point? o.o

2. anonymous

$f \prime(x)=e^x-3x^2$ solve f(x)=0 for all x's.. e^x-3x^2=0 is hard to be solved manually. is this a first course in calculus?

3. anonymous

i know that is what you have to do, i just dont want to do it.

4. nowhereman

let the computer work for you ;-)

5. anonymous

lol.. are you sure of the problem you gave anyway? is it x^3?

6. anonymous

i typed it correctly. it is e raised to the x minus x raised to the third.

7. anonymous

since you just want to the answer, I used a software program and found that it has three critical points.

8. anonymous

yeah, i just figured it out because i got tired of waiting, thanks though

9. anonymous

It's not really that hard.. $e^x - 3x^2 = 0 \rightarrow e^x = 3x^2 \rightarrow x = ln{3} + 2ln{x}$

10. anonymous

Then just graph both those functions and find where they intersect.

11. anonymous

wow, polpak, arent you impressive

12. anonymous

Yes, but not because of this.. ;p

13. anonymous

yeah right I didn't think of graphing method.. but I think it's easier to graph e^x=3x^2

14. anonymous

I like the other graph cause e^x grows so fast it's hard to see where they intersect, y=x and lnx are much closer to the origin by comparison.

15. anonymous

^^ good point