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Question

# Find the equation of the normal line to the curve $f(x)=2 x^3-3 x+1$ at the point $(1,0)$.

Solution

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In order to find the equation of a normal line, first differentiate the given function to obtain the derivative function.

Differentiating $f(x)$ with respect to $x$ yields

\begin{aligned} f'(x) &= \dfrac{d}{dx}\left( 2x^3 - 3x + 1 \right)\\ &= 2 \cdot 3x^2 - 3\\ &= 6x^2 - 3\\ &= 3(2x^2-1). \end{aligned}

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