Increasing and decreasing functions

Question 1

How do you know if a function is increasing?

Answer 1

If dy/dx > 0

Question 2

How do you know if a function is decreasing?

Answer 2

dy/dx < 0

Question 3

Steps of how to work out “show that the function is increasing for all values of x”

Answer 3

Eg show that f(x)=x^3+6x^2+21x+2 is increasing

1) Write increasing when f’(x)>0
2) Differentiate to find f’(x)
3) Complete the square
4) Statement

Question 4

Steps of how to work out “find the interval on which the function is decreasing”

Answer 4

1) Write decreasing when f’(x)<0
2) Differentiate to find f’(x)
2) Solve quadratic equation - find values of x
3) Write it as inequality