Word Prolems and Rate-of-Change
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Find 3rd derivative
f(x)= 3/16x^2
Find the indicated value
f(x)= 9-x^2 value f''(-sq rt 5)
Find f'''(x)
f''(x)=2x-2/x
Find the second derivative and solve the equationf''(x)=0
f(x)=x/x^2+1
The velocity of an object in meters per second is
v(t)=36-t, 0<t<6
Find the velocity and acceleration of the object when t=3. What can be said about the speed of the object when the velocity and acceleration have oppsite signs?
A brick becomes dislodged from the top of the empire state building (at a height of 1250) and falls to the sidewalk below.
a.) Write the position function of the brick.
b.) Write the velocity and acceleration functions.
c.) How long does it take the brick to hit the side walk?
d.) How fast is the brick traveling when it hits the side walk?
The velocity (in feet per second) of an automobile starting from rest is modeled by
ds/dt=90t/t+10
Complete a table, showing the velocity and acceleration at 10-sec intervals during the first min of travel. What can you conclude?
t 0 10 20 30 40 50 60
ds/dt
d^2s/dt^2
True or false, determine and explain why, if false.
if y=(x+1)(x+2)(x+3)(x+4), than d^5y/dx^5=0
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Solution Summary
Fourteen Derivative Problems involving Word Problems, Velocity, Acceleration and Rate-of-Change are solved. The solution is detailed and well presented.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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