Practice Second Derivative Test - 4.3 | 8. Application of Calculus | ICSE 12 Mathematics
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Second Derivative Test

4.3 - Second Derivative Test

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

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

💡 Hint: Set the first derivative f'(x) equal to zero.

Question 2 Easy

What does it mean if f''(c) > 0?

💡 Hint: Think about concavity.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What indicates a local maximum in the Second Derivative Test?

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

💡 Hint: Think about how concavity relates to maxima.

Question 2

True or False: The Second Derivative Test can always definitively classify critical points.

True
False

💡 Hint: Consider scenarios when the second derivative doesn't provide clarity.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function f(x) = x^4 - 4x^3 + 4x, find and classify all of its critical points.

💡 Hint: Calculate the first and second derivatives.

Challenge 2 Hard

Using the function f(x) = x^3 - 9x + 7, determine if there exist any points of inflection.

💡 Hint: After calculating the second derivative, remember to check signs in the intervals.

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