Practice Definition - 6.1 | 8. Application of Calculus | ICSE 12 Mathematics
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Definition

6.1 - Definition

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define an increasing function.

💡 Hint: Think about comparing values of the function.

Question 2 Easy

What does it mean for a function to be decreasing?

💡 Hint: Look at how the function's value changes.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What denotes a function as increasing?

f'(x) < 0
f'(x) > 0
f'(x) = 0

💡 Hint: Think about how derivative signs affect function behavior.

Question 2

True or False: A local maximum occurs where the derivative changes from negative to positive.

True
False

💡 Hint: Visualize how the function behavior changes at those points.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

You have a rectangular garden that must have a total perimeter of 100 meters. What dimensions yield the maximum area?

💡 Hint: Use the perimeter equation to express area as a function of one variable.

Challenge 2 Hard

Analyze f(x) = -x^4 + 4x^2. Find the local extrema and classify them.

💡 Hint: Use first and second derivative tests to classify all critical points.

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