# Word Prolems and Rate-of-Change

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

https://brainmass.com/math/derivatives/world-problems-rate-of-change-38085

#### Solution Summary

Fourteen Derivative Problems involving Word Problems, Velocity, Acceleration and Rate-of-Change are solved. The solution is detailed and well presented.