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Find the equation of the line tangent to the graph f(x) = -0.5x3 - 4x2 + 2x – 6 at the point (-6, -54).

User Hilarl
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1 Answer

23 votes
23 votes

To find the slope of the line, we start by calculating the first derivative of the function, as following:


\begin{gathered} f(x)=-0.5x^3-4x^2+2x-6 \\ \rightarrow f^(\prime)(x)=-1.5x^2-8x+2 \end{gathered}

The slope of the line tangent to the graph at (-6, -54) is:


f^(\prime)(-6)=m=-100

Then, we use the slope-point form to find the equation:


\begin{gathered} y+54=-100(x+6) \\ \rightarrow y+54=-100x-600 \\ \rightarrow y=-100x-654 \end{gathered}

User Pingoo
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