What are increasing and decreasing functions?

• A function, f(x), is?increasing?if?f'(x)?>?0
  • This means the value of the function (‘output’) increases as x increases
• A function, f(x), is?decreasing?if?f'(x)?<?0
  • This means the value of the function (‘output’) decreases as x increases
• A function, f(x), is?stationary?if?f'(x)?=?0

How do I find where functions are increasing, decreasing or stationary?

• To identify the?intervals?on which a function is increasing or decreasing

• Most functions are a combination of increasing, decreasing and stationary
  • a range of values of x (interval)?is given where a function satisfies each condition

What is a tangent?

• At any point on the graph of a (non-linear)?function, the?tangent?is the straight line that passes through that point and has the same?gradient?as the curve at that point

How do I find the equation of a tangent?

What is a normal?

• At any point on the graph of a (non-linear) function, the?normal?is the straight line that passes through and is?perpendicular?to the?tangent?at that point

How do I find the equation of a normal?Exam Tip

What are local minimum and maximum points?

How do I find the coordinates and nature of stationary points?