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anonymous

  • 5 years ago

calculate the number whose difference between itself and its square is a maximum

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  1. anonymous
    • 5 years ago
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    Incomplete info. as it is x-x^2=max

  2. anonymous
    • 5 years ago
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    how is the info incomplete?

  3. anonymous
    • 5 years ago
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    a maximum: a maximum means nothing in of itself, a maximum to what?!

  4. anonymous
    • 5 years ago
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    the maximum difference between any two real numbers

  5. anonymous
    • 5 years ago
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    sorry the maximmum difference between any number and its square

  6. anonymous
    • 5 years ago
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    for example for 0.8 the difference is .8 - .8^2 = .16

  7. watchmath
    • 5 years ago
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    Ok, so we want to maximize \(f(x)=x-x^2\) Without calculus: find the vertex \(x=-b/2a=-1/(2(-1))=1/2\). So it is maximum when \(x=1/2). With calculus, set \(f'(x)=1-2x=0\). Hence \(x=1/2\). Then you just need to justify that x=1/2 gives the maximum value.

  8. anonymous
    • 5 years ago
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    this is how i interpreted the question

  9. anonymous
    • 5 years ago
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    right! how the heck didn't i think of that - ty. how do i give medals?

  10. watchmath
    • 5 years ago
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    Press the good answer button :)

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spraguer (Moderator)
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