# Differential Calculus: How to find the slope of the curve $y=x(x+1)(x+2)$ at the points where it crosses the $x$-axis [closed]

Find the slope of the curve $$y=x(x+1)(x+2)$$ at the points where it crosses the $$x$$-axis.

• The curve crosses the x axis at $x = 0,-1,2$. Find $\frac{dy}{dx}$ and evaluate it at these points. – 1123581321 Feb 27 at 22:32
• Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. For instance, have you found the derivative? – N. F. Taussig Feb 27 at 23:14

$$y = x(x+1)(x+2)$$

First: where does it cross the $$x$$-axis? When $$y=0.$$

$$0=x(x+1)(x+2) \implies x=\{0,-1,-2\}$$

Now the slope at each point of the curve is given by: $$\dfrac{dy}{dy} = 3x^2+6x+2$$

So slopes are: $$\{2,-1,2\}$$ respectively.