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Applications of Derivatives

Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce

Practice quiz for Applications of Derivatives — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. MCQs and questions with answers to test your preparation.

45 questions20 flashcards4 concepts

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Quick Quiz: Applications of Derivatives

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Tap an answer to check it instantly. No sign-up needed for these 4.

1

Find the slope of the tangent to the curve y = x² + 3x - 2 at the point (1, 2).

2

For the function f(x) = x³ - 6x² + 9x + 1, find the intervals where f(x) is increasing.

3

Find the equation of the normal to the curve y = x² at the point (2, 4).

4

Find the maximum value of f(x) = 2x³ - 15x² + 36x - 10.

45 Questions·
multiple choicemultiple correct

Sample Questions

1multiple choice

If the demand function is D = 100 - 2P, find the elasticity of demand when P = 20.

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2/3

Step 1: When P = 20, D = 100 - 2(20) = 60. Step 2: dD/dP = -2. Step 3: η = -P/D × dD/dP = -20/60 × (-2) = 40/60 = 2/3.

2multiple correct

Which of the following statements about the function f(x) = x⁴ - 8x² + 5 are correct?

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f has minimum at x = ±2, f has maximum at x = 0, f is decreasing on (0, 2)

Step 1: f'(x) = 4x³ - 16x = 4x(x² - 4) = 4x(x-2)(x+2). Critical points: x = 0, ±2. Step 2: f''(x) = 12x² - 16. f''(0) = -16 < 0 (maximum), f''(±2) = 32 > 0 (minimum). Step 3: f'(x) < 0 on (0,2), so decreasing.

3multiple choice

For what value of x does the function f(x) = x³ - 3x² + 2 have a local minimum?

Show answer

x = 2

Step 1: f'(x) = 3x² - 6x = 3x(x - 2). Critical points: x = 0, 2. Step 2: f''(x) = 6x - 6. Step 3: f''(0) = -6 < 0 (maximum), f''(2) = 6 > 0 (minimum). Local minimum at x = 2.

4multiple choice

The cost function is C(x) = x² + 4x + 100. Find the marginal cost when x = 5.

Show answer

14

Step 1: Marginal cost = dC/dx = d/dx(x² + 4x + 100) = 2x + 4. Step 2: When x = 5, marginal cost = 2(5) + 4 = 14.

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Frequently Asked Questions

What are the important topics in Applications of Derivatives for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Applications of Derivatives covers several key topics that are frequently asked in Maharashtra Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Applications of Derivatives — Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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