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t the position of the ball at any timet is given bys(t) = -16t2 + 32t + 48, answer the %3D stions. What is the average velocity for the first five seconds the ball is in the air? What is the instantaneous velocity 1 seconds after the ball is thrown? Vhat is the height of the ball 1 seconds after the ball is thrown? t what time does the ball reach its maximum height? "hat is the maximum height of the ball? what time is the velocity of the ball 10 sec nat is the velocity of the ball when it hits the ground? at is the velocity of the ball when it reaches its maximum height? e a particle moves along the curve, such that time is in seconds and units are in - 8 for t 2 0. the velocity function.

t the position of the ball at any timet is given bys(t) = -16t2 + 32t + 48, answer the %3D stions. What is the average velocity for the first five seconds the ball is in the air? What is the instantaneous velocity 1 seconds after the ball is thrown? Vhat is the height of the ball 1 seconds after the ball is thrown? t what time does the ball reach its maximum height? "hat is the maximum height of the ball? what time is the velocity of the ball 10 sec nat is the velocity of the ball when it hits the ground? at is the velocity of the ball when it reaches its maximum height? e a particle moves along the curve, such that time is in seconds and units are in - 8 for t 2 0. the velocity function.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Find all points on the curve y = -x³ +-x* + 6x² where the tangent line is horizontal. 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given 0s x < 2n. 6. Find the equation of the line tangent to the graph of xy + y² = 4 at x = 3. 7. A ball is thrown up from the top of a 48-foot tower with initial velocity of 32 feet per second. Given that the position of the ball at any time t is given bys(t) = -16t2 + 32t + 48, answer the following questions. a. What is the average velocity for the first five seconds the ball is in the air? b. What is the instantaneous velocity 1 seconds after the ball is thrown? C. What is the height of the ball 1 seconds after the ball is thrown? d. At what time does the ball reach its maximum height? e. What is the maximum height of the ball? f. At what time is the velocity of the ball 10 sec g. What is the velocity of the ball when it hits the ground? h. What is the velocity of the ball when it reaches its maximum height? 8. Suppose a particle moves along the curve, such that time is in seconds and units are in feet, s(t) = t3 – 3t2 – 8 for t 2 0. a. Find the velocity function. b. Find the acceleration function. C. What is the position of the particle when the velocity is zero? d. What is the position of the particle when the acceleration is zero? е. What is the total distance traveled by the particle from the time it
Transcribed Image Text:4. Find all points on the curve y = -x³ +-x* + 6x² where the tangent line is horizontal. 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given 0s x < 2n. 6. Find the equation of the line tangent to the graph of xy + y² = 4 at x = 3. 7. A ball is thrown up from the top of a 48-foot tower with initial velocity of 32 feet per second. Given that the position of the ball at any time t is given bys(t) = -16t2 + 32t + 48, answer the following questions. a. What is the average velocity for the first five seconds the ball is in the air? b. What is the instantaneous velocity 1 seconds after the ball is thrown? C. What is the height of the ball 1 seconds after the ball is thrown? d. At what time does the ball reach its maximum height? e. What is the maximum height of the ball? f. At what time is the velocity of the ball 10 sec g. What is the velocity of the ball when it hits the ground? h. What is the velocity of the ball when it reaches its maximum height? 8. Suppose a particle moves along the curve, such that time is in seconds and units are in feet, s(t) = t3 – 3t2 – 8 for t 2 0. a. Find the velocity function. b. Find the acceleration function. C. What is the position of the particle when the velocity is zero? d. What is the position of the particle when the acceleration is zero? е. What is the total distance traveled by the particle from the time it
I. Vocabulary, Definitions and Concepts: Slope o the tangnt line 1. Differentiability at a point A 2. Continuity at a point 3. Instantaneous Rate of Change 4. Average Rate of Change 5. Definition of the Derivative 6. Squeeze Theorem 7. Derivative Rules: а. Constant Rule b. Power Rule С. Sum Rule d. Product Rule e. Quotient Rule f. Chain Rule g. Trigonometric Derivatives h. Derivatives of Logarithmic and Exponential Functions
Transcribed Image Text:I. Vocabulary, Definitions and Concepts: Slope o the tangnt line 1. Differentiability at a point A 2. Continuity at a point 3. Instantaneous Rate of Change 4. Average Rate of Change 5. Definition of the Derivative 6. Squeeze Theorem 7. Derivative Rules: а. Constant Rule b. Power Rule С. Sum Rule d. Product Rule e. Quotient Rule f. Chain Rule g. Trigonometric Derivatives h. Derivatives of Logarithmic and Exponential Functions
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