Practice First Derivative Test - 4.2 | Chapter 8 Application of Calculus | ICSE Class 12 Mathematics
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Find the critical points of f(x) = 2x^2 - 4x + 1.

πŸ’‘ Hint: Consider where the derivative changes signs.

Question 2

Easy

Is f(x) = x^2 increasing or decreasing at x = 1?

πŸ’‘ Hint: Check the derivative value at that point.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

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

Question 1

What does the First Derivative Test help to determine?

  • Where a function is constant
  • Local maxima and minima
  • Inflection points

πŸ’‘ Hint: Remember the test focuses on the behavior around critical points.

Question 2

True or False: If the derivative at a critical point is positive, the function has a local minimum.

  • True
  • False

πŸ’‘ Hint: Consider what it means for a function to be increasing or decreasing.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Find all critical points of f(x) = sin(x) on the interval [0, 2Ο€] and classify them.

πŸ’‘ Hint: The derivative of sin(x) is cos(x); set it to zero for critical points.

Question 2

A farmer wants to enclose a rectangular field with a fixed perimeter of 100m. What dimensions will maximize the area?

πŸ’‘ Hint: Use the area formula and derivative to find critical points.

Challenge and get performance evaluation