Exercises

Key Skills

IB Math AISL

Differentiation

Applications of the First Derivative

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Exercises

Key Skills

Applications of the First Derivative - Exercises | IB Math AISL | Perplex

Applications of the First Derivative

Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

Exercises

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Practice exam-style applications of the first derivative problems

Key Skills

Stationary points & Increasing/Decreasing Regions

SL 5.2

f′(x)⎩⎪⎨⎪⎧<0⇔f decreasing=0⇔f stationary>0⇔f increasing🚫

Maxima & Minima

SL AI 5.6

Stationary points are often local extrema.

If f′(a)=0, f is decreasing to the left of a (f′(x)<0), and f is increasing to the right of a (f′(x)>0), then (a,f(a)) is a local minimum.

If f′(a)=0, f is increasing to the left of a (f′(x)<0), and f is decreasing to the right of a (f′(x)>0), then (a,f(a)) is a local maximum.

Optimisation

SL AI 5.7

Optimisation problems require you to find a minimum or maximum value by producing a function f(x), taking its derivative, solving f′(x)=0, and confirming which stationary point(s) are minima or maxima.

Stationary points & Increasing/Decreasing Regions

SL 5.2

f′(x)⎩⎪⎨⎪⎧<0⇔f decreasing=0⇔f stationary>0⇔f increasing🚫

Maxima & Minima

SL AI 5.6

Stationary points are often local extrema.

If f′(a)=0, f is decreasing to the left of a (f′(x)<0), and f is increasing to the right of a (f′(x)>0), then (a,f(a)) is a local minimum.

If f′(a)=0, f is increasing to the left of a (f′(x)<0), and f is decreasing to the right of a (f′(x)>0), then (a,f(a)) is a local maximum.

Optimisation

SL AI 5.7