Maths with Lemon

Monotony

"What is mathematics? It is only a systematic effort of solving puzzles posed by nature."

Shakuntala Devi

Monotony (Min-Max)

What you have to know:

Key Points

  • 1. Watch the video:

Coronavirus and Inflection points

Another way of seeing the inflection point and concavity

  • In January 2020 there was an outbreak of the coronavirus. The whole world was going crazy that year. The deaths from the virus were rising up to some point and then started decreasing. The whole world was searching for the inflection point of the graph of the death rate.
  • 1. Watch the video:

Concavity / Inflection Points

What you have to know:

Key Points

  • 1. Watch the video:

IB questions on inflection points, minimum and maximum

What you have to know:

  • To find minimum or maximum of a function, take the first derivative equal to zero.
  • To find the inflection points, take the second derivative equal to zero and check the concavity.

Key Points

  • 1. Watch the video:

Extra

Material and references:

  • Hodder Book SL(ISBN: 9781510462359) :
    20D, 20E, 20F

Key Points

  • 1. How to interpret the second derivative of a function.

  • A function \( f(x) \) is:
    — concave-up where \( f''(x) > 0 \)
    — concave-down where \( f''(x) < 0 \)

  • 2. How to find local minimum and maximum points on a graph.

  • At a local maximum or minimum \(f'(x) = 0\)

  • Given \( f'(a) = 0 \) then if
    — \( f''(a) < 0 \) then there is a local maximum at \( x = a \)
    — \( f''(a) > 0 \) then there is a local minimum at \( x = a \)
    — \( f''(a) = 0 \) then no conclusion can be drawn

IB Past Paper Problems

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