calculus (rate of change)

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consider the function f(x)=x^2-6x+12

a. find the average rate of change over the interval [-1,3]

b. use the definition of the derivative to find f prime(x)

c. find the instantaneous rate of change at the point where x=3

d. find the value of x on the interval [-1,3] such that f prime(x) = -4

  • calculus (rate of change) -

    a.
    [ value of the function at 3 - value of the function at -1} / 4

    b.
    f(x+h) = x^2 + 2 x h + h^2 - 6x-6h +12
    f(x) = x^2 - 6x + 12
    f(x+h) -f(x) = 2xh +h^2 -6h
    divide by h
    2x + h - 6
    let h -->0
    2x - 6

    c.
    what is 2x-6 when x = 3 ???

    d.
    2x-6 = -4 when x = 1

    If you are having trouble with this, you should read the chapter on the subject more carefully. It is fundamental.

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