calculus ab acp review help?

1. F(x)= -ax^2 + bx and F has a relative maximum at (3,1) Find a -b .

2. for what value of K will F(x)= (8x+k) / (x^2) if it has a relative maximum at x=4 ..

3. suppose F(x)= x^4 + ax^2 what is the value of A if F has a local minimum at x= -2

please help me by showing me the steps as i dont understand how to do it. thanks in advance!!

1 Answer

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  • ?
    Lv 7
    1 decade ago
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    f (x) = -ax^2 + bx

    f ' (x) = -2ax + b <== f (x) is max or min when f ' (x) = 0

    -2ax + b = 0

    x = b / 2a

    . . . maximum at (3,1)

    b / 2a = 3

    6a - b = 0 <=== equation one

    1 = - a * 3^2 + b * 3

    1 = - 9a + 3b

    9a - 3b = -1 <=== equation two

    Two equations with two unknowns ...

    solve for a and b

    a = 1/9

    b = 2/3

    a - b = 1/9 - 2/3 = - 5/9

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