16. The displacement, in feet, of an object is given by by s(t) = -2t² + 4 where t is measured in seconds. (a) Fill in the table below for the appropriate average velocities. Don't round until the end of your calculations, then round to five decimal places. Time Interval [0, 1] [0.5, 1] [0.9, 1] [1, 1.1] [1, 1.5] [1, 2] ~2 -3 -3.8-4.2-s -6 Average Velocity (b) Make a conjecture about the instantaneous velocity of the object after 1 second. Explain your answer. 17. Use the definition of a derivative to find f'(x) if f(x)=√√-2x +3 18. Find the equation of the tangent line to f(x) = 3x - 10 at x = 1. Write your answer simplified and in the form y = mx + b. Then sketch a graph of y = f(x) and its tangent line at x = = 1. f'(x) = 2x + 3(1)-0 y₁ = f(1) = (1 2² +3 (1)-10=6 :6 f(x) = 2x +3 SUD -7/11+3=5
16. The displacement, in feet, of an object is given by by s(t) = -2t² + 4 where t is measured in seconds. (a) Fill in the table below for the appropriate average velocities. Don't round until the end of your calculations, then round to five decimal places. Time Interval [0, 1] [0.5, 1] [0.9, 1] [1, 1.1] [1, 1.5] [1, 2] ~2 -3 -3.8-4.2-s -6 Average Velocity (b) Make a conjecture about the instantaneous velocity of the object after 1 second. Explain your answer. 17. Use the definition of a derivative to find f'(x) if f(x)=√√-2x +3 18. Find the equation of the tangent line to f(x) = 3x - 10 at x = 1. Write your answer simplified and in the form y = mx + b. Then sketch a graph of y = f(x) and its tangent line at x = = 1. f'(x) = 2x + 3(1)-0 y₁ = f(1) = (1 2² +3 (1)-10=6 :6 f(x) = 2x +3 SUD -7/11+3=5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Use
limits to justify all of your results. Then sketch a graph of the function g(z) using
the information you found and the x and y intercepts.
g(x)
9(¹) =
16. The displacement, in feet, of an object is given by by s(t) -2t² + 4 where t is
measured in seconds.
(a) Fill in the table below for the appropriate average velocities. Don't round until
the end of your calculations, then round to five decimal places.
Time Interval
[0, 1] [0.5, 1] [0.9, 1] [1, 1.1] [1, 1.5] [1, 2]
1-6
~2
-3
-3.8-4.2 -S
Average Velocity
(b) Make a conjecture about the instantaneous velocity of the object after 1 second.
Explain your answer.
17. Use the definition of a derivative to find f'(x) if f(x)=√√-2x+3
18. Find the equation of the tangent line to f(x)=x² + 3x - 10 at x = 1. Write your
answer simplified and in the form y = mx +b. Then sketch a graph of y = f(x) and
its tangent line at x = 1.
y₁ = f(1) =(2²+3 (1)-10=6
f'(x) = 2x²+3 (1)-0
f(x) = 2x +3
-6
9F
MAT 201 X=-6
f(1) = 2(1) +3=5
y=(-6)= 5(x-1)
y-(-6)= Sx-5
m=s
Page 5 of 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7dcbfcd-ec40-4419-b8e9-2a693a942e70%2F1f4e8bab-2d2a-4e5d-ade7-bd76be04108a%2Fn4czyfg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use
limits to justify all of your results. Then sketch a graph of the function g(z) using
the information you found and the x and y intercepts.
g(x)
9(¹) =
16. The displacement, in feet, of an object is given by by s(t) -2t² + 4 where t is
measured in seconds.
(a) Fill in the table below for the appropriate average velocities. Don't round until
the end of your calculations, then round to five decimal places.
Time Interval
[0, 1] [0.5, 1] [0.9, 1] [1, 1.1] [1, 1.5] [1, 2]
1-6
~2
-3
-3.8-4.2 -S
Average Velocity
(b) Make a conjecture about the instantaneous velocity of the object after 1 second.
Explain your answer.
17. Use the definition of a derivative to find f'(x) if f(x)=√√-2x+3
18. Find the equation of the tangent line to f(x)=x² + 3x - 10 at x = 1. Write your
answer simplified and in the form y = mx +b. Then sketch a graph of y = f(x) and
its tangent line at x = 1.
y₁ = f(1) =(2²+3 (1)-10=6
f'(x) = 2x²+3 (1)-0
f(x) = 2x +3
-6
9F
MAT 201 X=-6
f(1) = 2(1) +3=5
y=(-6)= 5(x-1)
y-(-6)= Sx-5
m=s
Page 5 of 5
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