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32 – Applications of the Derivative No Calculator
Derivative Investigations 32 – Applications of the Derivative No Calculator
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Equation of tangent line to f(x) at x = a:
Slope of a normal line to f(x) at x = a: 1. Find the equation of the line tangent to f(x) at x = 1. 2. Find the equation of the line normal to f(x) at x = 2.
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3. Find the equation of the line tangent to g(x) at x = 2.
4. Find the equation of the line normal to g(x) at x = –1.
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5. Find the equation of the line tangent to h(x) at x = 0.
6. Find the equation of the line normal to h(x) at x = 1.
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DERIVATIVE POSITION s(t) VELOCITY v(t) ACCELERATION a(t) SLOPE AREA X
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A ball is thrown straight down from the top of a 100 foot tall building with an initial
velocity of Use the position function for free-falling objects: 7. Determine the position function of the ball. 8. Find v(2). Include units in your answer. 9. Find a(3). Include units in your answer.
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Given 10. Find the initial position. 11. Find the initial velocity. 12. Find the average velocity on the interval [0, 2]. 13. Find a(1).
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Given 14. Find a(1). 15. Find the average acceleration on the interval [0, 3].
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Given 16. Find the average velocity on [0, 2]. 17. Find the velocity at t = 2. 18. Find the average acceleration on [0, 2]. 19. Find the acceleration at t = 2.
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