6.26. Find the equations of the tangent and normal to the curve $y=f(x)=2 x^{3}-x-4$ at the point $x_{0}=1$.
Solution. Let's find the derivative and calculate its value and the value of the function at the given point: $f^{\prime}(x)=6 x^{2}-1$, $f(1)=-3, f^{\prime}(1)=5$.

The equation of the tangent line is $y=-3+5 \cdot(x-1)=5 x-8$. The equation of the normal line is $y=-3-(1 / 5)(x-1)=-0.2 x-2.8$.