Increasing/decreasing functions, stationary values and optimisation

Question 1

A function is increasing when?

Answer 1

f’(x)>0

Question 2

A function is decreasing when?

Answer 2

f’(x)<0

Question 3

A function is stationary when?

Answer 3

f’(x)=0

Question 4

How to show that a function is always increasing (decreasing)?

Answer 4

Differentiate then complete the square to show that f’(x)>0 (f’x)<0 for all values of x

Question 5

How do you find the solution to an optimisation?

Answer 5

Investigate stationary points/ and end points if necessary, always do Part B

Question 6

What do you get if you differentiate distance?

Answer 6

Speed

Question 7

What do you get if you differentiate speed?

Answer 7

Acceleration