Introduction to Derivatives
This worksheet covers fundamental concepts and applications of derivatives for Grade 11 calculus students.
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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. In your own words, explain what a derivative represents graphically and conceptually.
2. The derivative of a constant function f(x) = c is .
3. According to the Power Rule, if f(x) = x^n, then f'(x) = .
4. Which of the following is the derivative of f(x) = 3x^2 + 5x - 7?
6x + 5
3x + 5
6x + 5 - 7
6x^2 + 5x
5. The derivative of sin(x) is:
cos(x)
-cos(x)
tan(x)
sec(x)
6. Find the derivative of the function g(x) = 4x^3 - 2x^2 + x - 1.
7. If the position of a particle is given by s(t) = t^2 + 3t, find the velocity function v(t).
8. The derivative of a product of two functions is the product of their derivatives.
True
False