Stationary points

Question 1

Steps for finding stationary points

Answer 1

Firstly we differentiate the function
Then find stationary points by solving f’(x) = 0 and state at stationary points f’(x) =0
This should make brackets that we invert to get our x values.
Put these x values into undifferentiated equation and find y values of stationary points. And state points
We then put out x values into a nature table and find the nature of the stationary points.

Question 2

Nature table

Answer 2

Set out as two vertical line with a horizontal line at the top. Each line sticks out slightly.
On the left hand side above the horizontal line we have x, and between the lines we have the lowest x value and to the right the highest x value.
Below the horizontal on the left we have f’(x) and below that we have shape of graph.
At the front and back of each x value there should be an arrow : ——>
Now below each of the functions we need to have a value that is slightly lower and higher than the x value, and put those into the f’(x) equation, and see if it is positive or negative, and draw the symbol before and after the 0 (which is under the x value on the f’(x) line.
Then underneath the positive negative or 0 draw a line / if positive— if 0 and \ if negative.