Differentiation (C8)

Question 1

How do you differentiate to find the gradient at a point?

Answer 1

1) Rearrange the equation into powers of x.

2) Put your value of x into the function to find the gradient at that point on the graph.

Question 2

How do you figure out the stationary points of a function?

Answer 2

1) First differentiate the function.
2) ) Set this derivative equal to 0 and solve the equation for the values of x.
3) Put these x values back into the original equation to find the coupling y values.

Question 3

How do you decide if stationary points your given are minimum or maximum points?

Answer 3

1) Find the second order derivative of the function by differentiating twice.
2) Then put in the values of x in the stationary points into the second derivative.
3) If the answer is negative, then it is a maximum.
4) If the answer is positive, then it is a minimum.
5) If the answer is 0, then its a flat.