Given that $\displaystyle \frac{dy}{dx}=6(x-1)(x-2)$ and the coordinates of the stationery points are $\displaystyle (1,1)$ and $\displaystyle (2,0)$, determine the nature of these stationery points.
The answer is either minimum point, maximum point or a point of inflexion.
The answer can be derived by substituting in values which are < and > the x-coordinate of the stationery point to determine if the stationery point is a maximum, minimum or a point of inflexion.
However, the answer I have gotten does not tally with the answer from the book.
okay, here is an example...
If by substituting values of x < x-coordinate into dy/dx, you get a negative gradient, this means that it is down sloping.
If by substituting values of x > x-coordinate into dy/dx, you get a positive gradient, this means that it is up sloping.
So we can conclude that the x-coordinate point is a minimum point as the gradient is negative before increasing after the stationery point where dy/dx=0.
Yes, now here is your function: dy/dx= 6(x-1)(x-2).
If x< 1, both x- 1 and x- 2 are negative. What does that tell you about their product?
If 1< x< 2, x- 1 is positive while x- 2 is negative. What does that tell you about their product?
If 2< x, both x- 1 and x- 2 are positive. What does that tell you about their product?