Practice First Derivative Test - 2.1 | 5. Maxima and Minima | IB Class 10 Mathematics – Group 5, Calculus
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Academics

Grades

Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Curriculum

CBSE ICSE IB
Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Professional Courses
Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

games
Typing
Memory
Math
English Adventures
Knowledge

2.1 - First Derivative Test

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take mock test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Identify the critical points of f(x) = x^3 - 3x^2 + 4.

💡 Hint: Start by calculating the first derivative.

Question 2

Easy

What does it mean if the first derivative does not change sign at a critical point?

💡 Hint: Think about what happens when the function continues to increase or decrease.

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 is the First Derivative Test used for?

  • To find second derivatives
  • To classify critical points
  • To determine intervals of increase only

💡 Hint: Consider what the name implies about its function.

Question 2

If f'(x) changes from positive to negative at x = c, what can we conclude?

  • True
  • False

💡 Hint: A peak point generally implies a change in direction.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider the function f(x) = x^4 - 8x^3 + 18x^2. Use the First Derivative Test to identify critical points and classify them.

💡 Hint: Be careful to check signs on either side of your critical points!

Question 2

Create a real-world problem involving optimization—design a garden that maximizes area given a fixed perimeter. Formulate it and solve using derivatives.

💡 Hint: Sketching or visualizing the scenario can help solidify how we use these concepts in practice.

Challenge and get performance evaluation