Calc-slopes & concavity

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1. Let f(x)=x^3-3x+2

a.) Find the equation of the line tangent to the graph of y=f(x) at x=2

b.) For what values of x is the function increasing?

c.) For what values of x is the graph concave down?

  • Calc-slopes & concavity -

    f' = slope = 3 x^2 - 3
    at x = 2
    m = f'(2) = 3*8-3 = 21
    y = 21 x + b
    if x = 2, y = 8-6+2 = 4
    4 = 21(2) + b
    4 = 42 + b
    b = -38
    so
    y = 21 x - 38

    b.
    3 x^2 - 3 where is that + ???
    with big + or - x, slope big +
    0 = 3 x^2 - 3
    x = +/- 1
    so only - between -1 and + 1
    -1> x >1

    c.
    where is f" negative?
    f"(x) = 6x
    for negative x f"(x) is negative

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