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Resposta:
Let's simplify the given function:
[tex]y = x^{2} - 6x^{3} + 13x^{2} - 10x + 5\\y = -6x^{3} +14x^{2} - 10x + 5[/tex]
The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point. Thus:
[tex]y' = -18x^{2}+28x - 10\\y'(0) = -10[/tex]
The line intercept on the y-axis is 5. Thus, the equation of the tangent line is:
[tex]y = mx + b\\y = -10x + 5[/tex]
From analytic geometry, the slope of any line perpendicular to a line with slope m is the negative reciprocal −1/m. Thus, the equation of the normal line is:
[tex]y = mx + b\\y = \frac{1}{10}x + 5[/tex]