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find the numerical deriviative of the given function at the indicated point. use h=0.001. is the function differentiable at the indicated point?

4x- x^2, x=0

  • math -

    Looks like you are starting the concept of a derivative and are finding it by First Principles

    f(0) = 0
    f(0+.001) = .003999

    so the slope of the secant
    = (.00399 - 0)/(.001 - 0)
    = 3.999

    as you make your value of h get closer to zero, the slope of the secant will approach the slope of the tangent (the derivative) and it will get closer and closer to 4.

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