Determining value of k (calculus)

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For this question I know I have to take the derivative of the curve but do I equate it to the line to find k?

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1 Answer

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Solve for $y$ in terms of $x$. Then find $dy/dx$ and set it equal to the slope of the tangent line (which will be -1).

$$\frac{dy}{dx} = \frac{d}{dx}\left( -x + k\right) = -1$$

You should also draw a picture of the graph, it will make it easier to visually see what is going on, instead of just doing the algebra "blinded".

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