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10 July, 02:13

Determine the critical values of f (x) = ax² + bx + c.

A critical value can occur where f' (x) = 0 and also where f' (x) does not exist. Since f' (x) is a polynomial, there are no x-values where f ' (x) does not exist. Therefore, the only critical values will be where f' (x) = 0.

Solve the equation f' (x) = 0 for x.

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  1. 10 July, 05:50
    0
    x = - b / (2a)

    Step-by-step explanation:

    Using the power rule for derivatives, you can find ...

    f' (x) = 2ax + b

    Solving for x when f' (x) = 0, we have ...

    2ax + b = 0

    2ax = - b

    x = - b / (2a)

    The critical value is x = - b / (2a).
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Home » Mathematics » Determine the critical values of f (x) = ax² + bx + c. A critical value can occur where f' (x) = 0 and also where f' (x) does not exist. Since f' (x) is a polynomial, there are no x-values where f ' (x) does not exist.
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