the function f(x) = e^x - x^3 has how many critical points?

Question

anonymous · Answer

What is critical point? o.o

anonymous · Answer

$$f \prime(x)=e^x-3x^2$$
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?

bri · Answer

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

nowhereman · Answer

let the computer work for you ;-)

anonymous · Answer

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

bri · Answer

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

anonymous · Answer

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

bri · Answer

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

anonymous · Answer

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

anonymous · Answer

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

bri · Answer

wow, polpak, arent you impressive

anonymous · Answer

Yes, but not because of this.. ;p

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

^^
good point