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suppose f(x) is a function such that f(3)=5, f'(3)=0, and f''(3)=3. Is the point (3, 5) a relative maximum, minimum or inflection point?

  • calculus -

    f ' (3) = 0 tells me that at the point (3,5) the tangent is horizontal, so (3,5) must be either a maximum or a minimum.
    f '' (3) = 3 tell sme that at the point (3,5) the curve is concave up, so

    (3,5) must be a minimum point.

    (it couldn't possibly be a point of inflection or else the f '' (3) would have been 0 )

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