Practice Application of Derivatives - 3.6 | 3. Calculus | ICSE 12 Mathematics
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Application of Derivatives

3.6 - Application of Derivatives

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the equation of the tangent line at a point P(x₁, y₁) if the slope is m?

💡 Hint: Use the point-slope form of the linear equation.

Question 2 Easy

True or False: The slope of the normal line is the negative reciprocal of the slope of the tangent line.

💡 Hint: Recall the relationship between perpendicular slopes.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the derivative represent?

The area under a curve
The rate of change at a point
The maximum value of a function

💡 Hint: Think about how we perceive change in motion.

Question 2

True or False: A point is a local maximum if the first derivative is zero and the second derivative is positive.

True
False

💡 Hint: Remember the conditions for maximum and minimum.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A rectangular garden has dimensions x and y. The area A = xy = 100. Express y in terms of x and find dimensions that minimize the perimeter.

💡 Hint: Optimize the perimeter as a function of area.

Challenge 2 Hard

A company's cost function is C(x) = x³ - 5x² + 8x + 15. Determine the number of units produced for minimized cost.

💡 Hint: Use both derivatives to confirm minimum value.

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