Differentiation and its Applications
CBSE · Class 12 · Applied Mathematics
Most important questions from Differentiation and its Applications for CBSE Class 12 Applied Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Sample Questions
Find the second derivative of y = x³ - 6x² + 9x
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6x - 12
First derivative: dy/dx = 3x² - 12x + 9. Second derivative: d²y/dx² = 6x - 12.
If the cost function is C(x) = x² + 10x + 50, find the marginal cost when x = 5
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20
Marginal cost = dC/dx = 2x + 10. At x = 5: MC = 2(5) + 10 = 20.
Find the slope of the tangent to y = x² + 3x at the point (2, 10)
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7
Slope of tangent = dy/dx = 2x + 3. At x = 2: slope = 2(2) + 3 = 7.
Which of the following are true for the function f(x) = x³ - 3x? (Select all correct answers)
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f'(x) = 3x² - 3, f'(1) = 0, f'(-1) = 0, f has critical points at x = ±1
f'(x) = 3x² - 3. Setting f'(x) = 0: 3x² - 3 = 0, so x² = 1, giving x = ±1. At these points, f'(1) = f'(-1) = 0. At x = 0, f'(0) = -3, not 3.
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