Math (Calculus)

The function f(x)=-2x^3+10.2x^2+202.275x+0.87
is increasing on the open interval (?,?).
It is decreasing on the open interval (-oo,?) and the open interval (?,+oo)
The function has a local maximum at ?

I used derivative
-6x^2+20.4x+202.275 and find the root but it doesn't work with this problem.

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  1. Yes, it does work,

    let's set
    -6x^2+20.4x+202.275 = 0
    6x^2 - 20.4x - 202.275 = 0
    I used the formula and got
    x = 7.75 or x = -4.35

    remember that the function is increasing when the derivative is postive, and decreasing when ....

    so the function is increasing for
    -4.35 < x < 7.75
    and decreasing for
    x < -4.35 OR x > 7.75

    You should have a general idea what a function like
    f(x) = -2x^3 + ... looks like
    so x = 7.75 will produce a local maximum.
    Plug x = 7.75 into f(x) to find that local maximum

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    posted by Reiny

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