IB DP Maths: AI SL复习笔记5.1.2 Applications of Differentiation
ncreasing & Decreasing Functions
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
STEP 1 Find the derivative f'(x)
STEP 2 Solve the inequalities f'(x) > 0 (for increasing intervals) and/or f'(x) < 0 (for decreasing intervals)
- 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
Worked Example
Tangents & Normals
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
Worked Example
Local Minimum & Maximum Points
What are local minimum and maximum points?
How do I find the coordinates and nature of stationary points?
Worked Example
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