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anonymous

  • one year ago

MEDAL!!!!!!!!! Functions f(x) and g(x) are shown below:

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  1. anonymous
    • one year ago
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    f(x) = 3x2 + 12x + 16 g(x)

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  2. anonymous
    • one year ago
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    Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value

  3. welshfella
    • one year ago
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    for f(x) value of x at minimum is -b/2a ( that the a and b in the function ax^2 + bx + c) Then plug this into the formula for f(x) to get minimum value of f(x)

  4. anonymous
    • one year ago
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    g "(x) = -16sin(4x - π) > 0 for x = 5π/8, etc. So therefore, g(5π/8) = 2sin(π/4) + 4 = 4 + √2 > f(-2) = 4

  5. welshfella
    • one year ago
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    For g(x) the minimum is at x = pi/2 so plug this into formula for g(x) to get the required minimum.

  6. anonymous
    • one year ago
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    so f(x) isf '(x) = 6x + 12 =0 => x = -2

  7. welshfella
    • one year ago
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    oh ok - you are using calculus now plug -2 into f(x)

  8. anonymous
    • one year ago
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    that equals 0

  9. welshfella
    • one year ago
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    No - try again

  10. welshfella
    • one year ago
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    its 4

  11. anonymous
    • one year ago
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    what about g(x)

  12. anonymous
    • one year ago
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    is that the smallest y value

  13. welshfella
    • one year ago
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    yes g(x) is smallest minimum value

  14. welshfella
    • one year ago
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    i get minimum value of g(x) = -2

  15. welshfella
    • one year ago
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    g(x) = 2 sin (x - pi) g'(x) = 2 cos ( x - pi) = 0 at turning points

  16. anonymous
    • one year ago
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    explain how to find the minimum value for each function

  17. welshfella
    • one year ago
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    using calculus you find the first derivative and equate it to zero and solve for x this will give you a critical point you can now test for maximum or minimum by taking the second derivative and finding its sign for the value of x you have found positive value is minimum and negative is a maximum.

  18. welshfella
    • one year ago
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    so for the first question f"(x) is 6 positive so thats a minimum

  19. anonymous
    • one year ago
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    thanks for the help man

  20. welshfella
    • one year ago
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    yw

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