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Math Help - slope of tangent line at point (4,f(4))

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    slope of tangent line at point (4,f(4))

    Consider the function f(x) = 3x^(3)-5x^(2)-6
    a) find [f(x+h) - f(x)]/h
    (I found: 9x^2 + 9xh+3h^2-10x-5h, which is correct)
    b) Find the derivative of f at x
    (I found: 9x^2 - 10x, which is correct as well)

    ***c)What is the slope of the tangent line to the graph of f at the point (4,f(4))?

    I don't know where to sub in these values, i tried substituting x=4 and y=4 into f(x) = 3x^(3)-5x^(2)-6 as well as 9x^2 + 9xh+3h^2-10x-5h to get the slope but in all honesty i don't have a clue
    what is the "slope of tangent line" equation? i thought it was [f(x+h) - f(x)]/h as h approaches 0-- yes? no?

    please help me out here,
    thanks
    Brittany
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    Quote Originally Posted by williamb View Post
    Consider the function f(x) = 3x^(3)-5x^(2)-6
    a) find [f(x+h) - f(x)]/h
    (I found: 9x^2 + 9xh+3h^2-10x-5h, which is correct)
    b) Find the derivative of f at x
    (I found: 9x^2 - 10x, which is correct as well)

    ***c)What is the slope of the tangent line to the graph of f at the point (4,f(4))?

    I don't know where to sub in these values, i tried substituting x=4 and y=4 into f(x) = 3x^(3)-5x^(2)-6 as well as 9x^2 + 9xh+3h^2-10x-5h to get the slope but in all honesty i don't have a clue
    what is the "slope of tangent line" equation? i thought it was [f(x+h) - f(x)]/h as h approaches 0-- yes? no?

    please help me out here,
    thanks
    Brittany
    The derivative tells you the slope of the graph at any point.

    So you found that the derivative of f is

    f'(x)=9x^2 - 10x so

    f'(4)=9(4)^2 - 10(4)=144-40=104
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