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  1. #1
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    tangent

    Given that the curve y = 5 + 4x -x^2 has a tangent equation in the form of y = mx + 9. Calculate the values of m without drawing a graph or using differentiation.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by z1llch View Post
    Given that the curve y = 5 + 4x -x^2 has a tangent equation in the form of y = mx + 9. Calculate the values of m without drawing a graph or using differentiation.
    the tangent line must have a point in common with the graph. so since y = 5 + 4x - x^2 on the graph, the y in y = mx + 9 must have the same value, so

    5 + 4x - x^2 = mx + 9

    moreover, the tangent line must touch only ONE point on the graph. so the m we want occurs when the discriminant of the above quadratic is zero
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  3. #3
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    Hello, z1llch!

    Given that the curve y \:= \:5 + 4x -x^2 has a tangent equation in the form: y \:= \:mx + 9,
    calculate the values of m without drawing a graph or using differentiation.

    If that line tangent to the parabola, they intersect at one point.

    We have: . mx + 9 \:=\:5 + 4x - x^2 \quad\Rightarrow\quad x^2 + (m-4)x + 4 \:=\:0

    Quadratic Formula: . x \;=\;\frac{-(m-4) \pm\sqrt{m^2-8m}}{2}


    There will be one point of intersection if the disriminant is zero.

    Hence: . m^2-8m \:=\:0\quad\Rightarrow\quad m(m-8) \:=\:0\quad\Rightarrow\quad\boxed{ m \:=\:0,\:8}

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