Introduction to Derivatives
Explore the fundamental concepts of derivatives, including limits, slopes of tangent lines, and basic differentiation rules.
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Introduction to Derivatives
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What does the derivative of a function represent graphically?
The area under the curve
The slope of the tangent line
The y-intercept of the function
The x-intercepts of the function
2. The process of finding the derivative of a function is called:
Integration
Differentiation
Factorization
Simplification
3. The derivative of a constant function is always .
4. The power rule states that if f(x) = x^n, then f'(x) = .
5. Explain in your own words what a limit is in the context of calculus.
6. The derivative of f(x) = 3x is 3.
True
False
7. A function must be continuous at a point to be differentiable at that point.
True
False
8. Find the derivative of the function f(x) = 5x^3 - 2x + 7 using the power rule.
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