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anonymous

  • one year ago

f(x) g(x)

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  1. marinos
    • one year ago
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    Do you mean the following functions ? \[f(x)=-4\left( x-6 \right)^{2}+3\] and \[g(x)=2\cos \left( 2x-\pi \right)+4\]

  2. anonymous
    • one year ago
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    yes @marinos

  3. anonymous
    • one year ago
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    The maximum of cosine is 1, then g max is 2+4=2 The the vertex of the flipped parabola is when is 0, cause it's negative otherwise. So f max is 0+3 =3

  4. anonymous
    • one year ago
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    can you explain how @Ahmad-nedal

  5. marinos
    • one year ago
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    Remember that a square is always non-negative and that the absolute value of (sine and) cosine function(s) is at most 1.

  6. anonymous
    • one year ago
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    But the thing is, these two values are not satisfied at the same x coordinate, I think you will now be needing calculus 1 to find that point where x gets you the maximum

  7. anonymous
    • one year ago
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    What is your grade right now @jacey.stewart ?

  8. anonymous
    • one year ago
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    You use equation x=-b/2a to find the maximum Im just confused on the cosine part

  9. anonymous
    • one year ago
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    B

  10. anonymous
    • one year ago
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    The maximum of any sinsouidal function (since, cosx) is 1, therefore the maximum of cosine is 2

  11. marinos
    • one year ago
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    We have that \[\left( x-6 \right)^{2}\ge0\] since it is a square. Therefore \[-4\left( x-6 \right)^{2}\le0\] so \[f(x)=-4\left( x-6 \right)^{2}+3\le3\] implying that the maximum value of the function \[f(x)\] is 3. Can you argue similarly for the other function ?

  12. anonymous
    • one year ago
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    In my opinion, I think the question is not well written. Again if the maximum of f and g are achieved in two different x coordinates. Thus you cannot determine which point gives you the maximum MULTIPLE OF F(X) AND G(X)

  13. anonymous
    • one year ago
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    I repeat, you may need deffrentiation to find the maximum of f times g

  14. anonymous
    • one year ago
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    Is what I'm saying make sense jacy?

  15. marinos
    • one year ago
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    @Ahmad-nedal No differentiation is needed for these functions. There maximum value can be obtained using inqualities.

  16. anonymous
    • one year ago
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    I think it ultimately asked for the maximum of the multiple of F and G, isn't she?

  17. marinos
    • one year ago
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    Since \[\cos \left( 2x-\pi \right)\le1\] we have \[2\cos \left( 2x-\pi \right)\le2\] so \[g(x)=2\cos \left( 2x-\pi \right)+4\le2+4=6\] therefore the maximum value of this function is 6, and it is the greatest of the maximum values of the two initial functions.

  18. marinos
    • one year ago
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    @Ahmad-nedal I didn't see any reference to the product of f(x) and g(x) (in which case you do need differentiation to find the max value)

  19. anonymous
    • one year ago
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    Then you are right, it will be kinda trevial if considered two separate questions Thanksfor clarification

  20. marinos
    • one year ago
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    You are welcome.

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