# Thread: Differentiation & Stationary Points

1. ## Differentiation & Stationary Points

Having some trouble with the following two questions, I have an answer but it doesn't make sense...

A function f is defined by the formula f (x) = (x-1)^2 (x+2)

(a) Find the coordinates of the points where the curve with the equation y = f(x) crosses the x - and y-axes.

(b) Find the stationary points of this curve y = f(x).

For the derivative of (a) I got 2x^2 - 3 but I didn't know how to get the points from that... Help is much appreciated!

2. ## Re: Differentiation & Stationary Points

The derivative of F(x) is 3X2-5 .....That is your first mistake. unless of course your question writing wasn't correct (i.e. you missed out a + in between the two terms, but as you have written it, your derivative is wrong)
To find the points where it crosses the y axis you need to start with F(x) and subsitute x=0 to find all the points where it crosses the y axis.
To find the points crossing the x axis you need to sub in y = 0 and find the values of x that satisfy the equation. I can't tell you how many there are as i am not sure your question writing was correct.

To find stationary points you need to take the derivative equation and make it equal to zero (i.e. dy/dx = 0 and therefore showing that the gradient of the curve = 0, this is the meaning of a stationary point). You then need to solve the derivative equation for values of x that satisfy, but this time you need to substitute the values you get back into the original F(x) equation to find the value of the y coordinate.