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Consider the function.
f (x) = 5x3 + 3x
(a) Compute the derivative at x = 3 using the limit definition.
f '(3) =
(b) Find an equation of the tangent line.

  • calculus -

    evaluate f(3)
    evaluate (3+h) and simplify

    then take
    Limit [ (f(3+h) - f(3) ]/h as h --->0

    You should be able to factor out an h from the top which would then cancel the h in the bottom
    you should get
    f'(3) = 138

    b) when x=3, y = 138 (that's a coincidence)
    so you have
    slope of tangent is 138 and (3,138) is a point on it

    y = 138x + b , plug in the point
    138 = 138(3) + b
    b = -276

    so y = 138x - 276 is the tangent equation

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