Differentiation and its Applications — Practice Quiz
CBSE · Class 12 · Applied Mathematics
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Quick Quiz: Differentiation and its Applications
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Find dy/dx if y = 3x² + 5x - 7
If x² + y² = 25, find dy/dx using implicit differentiation
Find the derivative of y = e^(2x)
If x = t² and y = 2t, find dy/dx
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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- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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