Practice Differentiation - Basic Concepts - 3.1 | Chapter 3: Calculus | ICSE Class 12 Mathematics
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the derivative of f(x) = x²?

💡 Hint: Use the Power Rule.

Question 2

Easy

Using the Sum Rule, find the derivative of f(x) = 3x + 5.

💡 Hint: Differentiate each term separately.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the derivative f'(x) represent?

  • Rate of change
  • Value of function
  • Tangent length

💡 Hint: Think about how f(x) is changing.

Question 2

True or False: The Power Rule states that the derivative of xⁿ is nxⁿ⁻¹.

  • True
  • False

💡 Hint: Calculate the derivative and identify the coefficients.

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Challenge Problems

Push your limits with challenges.

Question 1

If the cost function is C(x) = 5x² + 4x + 50, find the marginal cost using differentiation.

💡 Hint: Take the derivative with respect to x.

Question 2

Given f(t) = 3t³ - 5t² + 2t, determine the points where local maxima and minima occur.

💡 Hint: Don't forget to check for second derivatives!

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