Question:

The number of points on the curve $y=54x^5-135x^4-70x^3+180x^2+210x$ at which the normal lines are parallel to $x+90y+2=0$ is:

Step-by-Step Solution

Key Concept: Normal slope $=-\frac{1}{90}$, so $\frac{dy}{dx}=90$. Differentiate: $270x^4-540x^3-210x^2+360x+210=90$.

4 points.

Correct Answer: 3