bri
  • bri
the function f(x) = e^x - x^3 has how many critical points?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What is critical point? o.o
anonymous
  • 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?
bri
  • bri
i know that is what you have to do, i just dont want to do it.

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nowhereman
  • nowhereman
let the computer work for you ;-)
anonymous
  • anonymous
lol.. are you sure of the problem you gave anyway? is it x^3?
bri
  • bri
i typed it correctly. it is e raised to the x minus x raised to the third.
anonymous
  • anonymous
since you just want to the answer, I used a software program and found that it has three critical points.
bri
  • bri
yeah, i just figured it out because i got tired of waiting, thanks though
anonymous
  • anonymous
It's not really that hard.. \[e^x - 3x^2 = 0 \rightarrow e^x = 3x^2 \rightarrow x = ln{3} + 2ln{x}\]
anonymous
  • anonymous
Then just graph both those functions and find where they intersect.
bri
  • bri
wow, polpak, arent you impressive
anonymous
  • anonymous
Yes, but not because of this.. ;p
anonymous
  • anonymous
yeah right I didn't think of graphing method.. but I think it's easier to graph e^x=3x^2
anonymous
  • 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.
anonymous
  • anonymous
^^ good point

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