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Math Help - slope and tangent lines

  1. #1
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    slope and tangent lines

    Let

    (a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

    (b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

    what method do I use to solve these problems and how do I solve them?
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  2. #2
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    Quote Originally Posted by Da Freak View Post
    Let

    (a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

    set f'(x) = 0 , solve for x, determine the function value(s) for each value of x

    (b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

    you need two things ... the point of tangency (0, f(0)) on the curve and the slope at that point, f'(0)

    y - f(0) = f'(0)(x - 0)


    what method do I use to solve these problems and how do I solve them?
    ...
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  3. #3
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    Quote Originally Posted by Da Freak View Post
    Let

    (a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

    (b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

    what method do I use to solve these problems and how do I solve them?
    (a) x-coordinate of points: Solve f'(x) = 0 for x.

    y-coordinate of points: Substitute above values of x into y = f(x).

    (b) The point has coordinates (0, -10) so (0, -10) is a known point on the tangent line.

    Calculate gradient = m = f'(0).

    So now you have a point and a gradient - if you're studying calculus you should certainly know how to get the equation of a line from these two things.
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