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bri

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    What is critical point? o.o

  2. anonymous
    • 5 years ago
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    \[f \prime(x)=e^x-3x^2\] 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. bri
    • 5 years ago
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    i know that is what you have to do, i just dont want to do it.

  4. nowhereman
    • 5 years ago
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    let the computer work for you ;-)

  5. anonymous
    • 5 years ago
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    lol.. are you sure of the problem you gave anyway? is it x^3?

  6. bri
    • 5 years ago
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    i typed it correctly. it is e raised to the x minus x raised to the third.

  7. anonymous
    • 5 years ago
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    since you just want to the answer, I used a software program and found that it has three critical points.

  8. bri
    • 5 years ago
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    yeah, i just figured it out because i got tired of waiting, thanks though

  9. anonymous
    • 5 years ago
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    It's not really that hard.. \[e^x - 3x^2 = 0 \rightarrow e^x = 3x^2 \rightarrow x = ln{3} + 2ln{x}\]

  10. anonymous
    • 5 years ago
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    Then just graph both those functions and find where they intersect.

  11. bri
    • 5 years ago
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    wow, polpak, arent you impressive

  12. anonymous
    • 5 years ago
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    Yes, but not because of this.. ;p

  13. anonymous
    • 5 years ago
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    yeah right I didn't think of graphing method.. but I think it's easier to graph e^x=3x^2

  14. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    ^^ good point

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