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?Find an equation of the tangent line to the curve at the given point.y = 2 (1,3)
Chapter 2, Problem 37(choose chapter or problem)
Find an equation of the tangent line to the curve at the given point.
\(y=2 x^{3}-x^{2}+2, \quad (1,3)\)
Questions & Answers
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QUESTION:
Find an equation of the tangent line to the curve at the given point.
\(y=2 x^{3}-x^{2}+2, \quad (1,3)\)
ANSWER:Step 1 of 3
Given function: \(y=2 x^{3}-x^{2}+2\)
Taking 1st derivative of the equations,
\(\begin{array}{l}
\frac{d y}{d x}=\frac{d}{d x}\left(2 x^{3}-x^{2}+2\right) \\
\frac{d y}{d x}=\left(2 \frac{d}{d x} x^{3}-\frac{d}{d x} x^{2}+\frac{d}{d x} 2\right) \\
\frac{d y}{d x}=2\left(3 x^{2}\right)-2 x+0 \\
\frac{d y}{d x}=6 x^{2}-2
\end{array}\)
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