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IB DP Maths: AI SL復(fù)習(xí)筆記5.1.2 Applications of Differentiation

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日 下午4:56

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

7.2.2-Incr-Decr-Illustr-1

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

1TmY~BKn_5-1-2-ib-sl-ai-aa-we1-soltn-a

JF~BDMqb_5-1-2-ib-sl-ai-aa-we1-soltn-b

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

7.2.1-Grad-Tang-Norm-Illustr-2

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

7.2.1-Grad-Tang-Norm-Illustr-3

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

Worked Example

5-1-2-ib-sl-ai-aa-we1-soltn-a

5-1-2-ib-sl-ai-aa-we1-soltn-b

Local Minimum & Maximum Points

What are local minimum and maximum points?

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

7.2.4-Stationary-Points-incr-decr-min-max

 

Worked Example

K2O1YEHT_5-1-2-ib-sl-ai-only-we2-soltn

 

 

 

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