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March 25, 2017

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Consider the quadratic function
f(x) = – x^2 + 10x – 26. Determine whether there is a maximum or
minimum value and find that value.

  • Algebra - ,

    This is algebra?

    If you have not learned differentiation, perhaps your teacher wants you to use a calculator to find the extrema. (If you have, disregard this paragraph).

    Take the derivative of f(x):
    f'(x)= -2x + 10

    Set f'(x) = 0
    -2x + 10 = 0
    10 = 2x
    x = 5

    Now use a sign line to find whether x=5 is a minimum or maximum.

    f'(0) = +
    f'(10) = -

    x=5 is a maximum because f'(x) changes signs from + to -

  • Algebra - ,

    complete the square,
    f(x) = – x^2 + 10x – 26
    = - [x^2 - 10x + 25 - 25] - 26
    = -(x-5)^2 + 25 - 26
    = -(x-5)^2 - 1

    so the vertex is (5,-1) and since the parabola opens downwards, it will be a maximum point and the maximum value of the function is -1

  • Algebra - ,

    I do not think these answers are right. I get somethin else and 5 is not an option. Here are the choices

    A. Minimum is 25
    B. Minimum is -51
    C. Maximum is -1
    D. Maximum us -51

  • Algebra - ,

    5 is the value at which the maximum occurs. f(5) = -1, so choice C.

  • Algebra - ,

    I was thinking that as well! Thanks!

  • Algebra - ,

    that is exactly the answer I gave you, read my last line of my reply please

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