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Math Help - f(x) increse or decrease

  1. #1
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    f(x) increse or decrease

    f(x)= -2x^3 + 5x^2 -3x +1
    Is f(x) increasing or decreasing when x=-2???
    I think its increasing?
    also does the f ' (x) and f '' (x) tell you the same thing about cubic fuctions than quadratic functions?

    I think the f ' (x) tells me the gradient of the tangent line and f''(x) tells if the turning point is max or min??
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by wolfhound View Post
    f(x)= -2x^3 + 5x^2 -3x +1
    Is f(x) increasing or decreasing when x=-2???
    I think its increasing?
    also does the f ' (x) and f '' (x) tell you the same thing about cubic fuctions than quadratic functions? f' and f" tell you the same thing about ALL functions. (in most cases)

    I think the f ' (x) tells me the gradient of the tangent line and f''(x) tells if the turning point is max or min?? Indeed.
    f'(x)=-6x^2+10x-3

    f'(-2)=-47

    Since -47 is less than 0, we conclude that f(x) is decreasing at x=-2
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  3. #3
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    Thanks on another question
    f(x)=x^2 -2x -8
    it says use the first derivative to find exact turning point of f(x)
    so f ' (x)= 2x-2
    so x =1?? is this correct
    so that means the turning point is (1,-8) and the other roots are (4,0) and (-2,0)?
    its seems to cut the yintercept at -6? I thought by looking at the constant -8 it woul cut there..

    Thanks
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by wolfhound View Post
    Thanks on another question
    f(x)=x^2 -2x -8
    it says use the first derivative to find exact turning point of f(x)
    so f ' (x)= 2x-2
    so x =1?? is this correct yes.
    so that means the turning point is (1,-9) and the other roots are (4,0) and (-2,0)? Other roots? These are the only roots to f (real).
    its seems to cut the yintercept at -6? I thought by looking at the constant -8 it woul cut there..

    Thanks
    .
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  5. #5
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    How is the turning point(1,-9)?
    and not (1,-8)?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by wolfhound View Post
    How is the turning point(1,-9)?
    and not (1,-8)?
    f(1)=(1)^2-2(1)-8=-9

    Therefore, your turning point is the point P=(1,-9)
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  7. #7
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    Thanks,never knew I should do that
    one more question please should the function cut the y intercept at -8(the constant in the original quadratic)
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by wolfhound View Post
    Thanks,never knew I should do that
    one more question please should the function cut the y intercept at -8(the constant in the original quadratic) yes. The y-intercept is (0,-8)
    .
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  9. #9
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    Thanks Dude!
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