Pure Mathematics · 3rd secondary · First Term

Calculus - Behaviour of the function and curve sketching — Maximum and minimum values

About this lesson

This unit teaches the concepts of critical points, local maximum and minimum values, and absolute extrema for continuous functions. It explains how to find critical points where the derivative is zero or undefined, and uses the first derivative test to determine whether a critical point is a local maximum, local minimum, or neither. The unit also covers finding absolute maximum and minimum values of a function on a closed interval by comparing function values at critical points and endpoints. Worked examples include polynomial, fractional, and exponential functions, with practice exercises for students.

Main topics in this lesson

Critical points
Local maximum and minimum values
First derivative test
Absolute extrema on a closed interval

Key terms and vocabulary

critical point
local maximum
local minimum
absolute extrema
first derivative test
stationary point
end point extrema

Questions and answers on Calculus - Behaviour of the function and curve sketching — Maximum and minimum values - practice and revision

Multiple choice questions on this lesson in Pure Mathematics for 3rd secondary, First Term, with practice exercises for revision and exam preparation.

إذا كانت f(x) = x³ − 3x² + 2، فإن للدالة قيمة عظمى محلية تساوي:

1 2
2 −2
3 0
4 1

إذا كانت f(x) = eˣ − x على الفترة المغلقة [−1، 1]، فإن القيمة الصغرى المطلقة للدالة تساوي:

1 1
2 e − 1
3 e⁻¹ + 1
4 0

إذا كانت f(x) = eˣ − x، فإن للدالة قيمة صغرى محلية تساوي:

1 1
2 0
3 e
4 −1

إذا كانت f(x) = x + 4/x، فإن للدالة قيمة صغرى محلية تساوي:

1 4
2 −4
3 2
4 0

إذا كانت f(x) = x + 4/x، فإن النقطة الحرجة للدالة توجد عند x تساوي:

1 2
2 −2
3 4
4 1

إذا كانت f(x) = x³ − 12x على الفترة المغلقة [−3، 3]، فإن القيمة العظمى المطلقة للدالة تساوي:

1 16
2 −16
3 9
4 −9

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