Calculate velocity and rate of change with derivative of f

Let f be defined as follows.
f(x)=x^2-3x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 6 to x = 7

from x = 6 to x = 6.5

from x = 6 to x = 6.1
(b) Find the (instantaneous) rate of change of y at x = 6.

The demand for Sportsman 5 X 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.)
p = f(x) = ?0.1x^2 ? x + 40
(a) Find the average rate of change in the unit price of a tent if the quantity demanded is between the following intervals.
between 4400 and 4450 tents $ per 1000 tents

between 4400 and 4410 tents $ per 1000 tents

(b) What is the rate of change of the unit price if the quantity demanded is 4400?
$ per 1000 tents

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the following function.
P=f(t)=3t^2+2t+1
Find the rate of population growth at t = 11 min.
bacteria per minute

The position function of an object moving along a straight line is given by
s = f(t).
The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a.

A ball is thrown straight up with an initial velocity of 144 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 144t ? 16t^2.
(a) What is the average velocity of the ball over the following time intervals?
[4,5] ft/sec

[4,4.5] ft/sec

[4,4.1] ft/sec

(b) What is the instantaneous velocity at time t = 4?
ft/sec

(c) What is the instantaneous velocity at time t = 8?
ft/sec
Is the ball rising or falling at this time?
rising falling

The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t)
To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t.
a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of

An object is thrown downward from the top of a building with an initial velocity of 30 m/s. Assuming a positive direction of y measured downward from the top, derive an expression for (a) the velocityand (b) the displacement as a function of time. Assume y(0)=0

The total solar radiation H on a particular surface during an average clear day is given by:
H=5000/T^2+10
where t (-6 < equal to or less than t < equal to or less than 6 ) is the number of hours from noon. Note that 6 a.m. is equivalent to t = -6. Find the instantaneous rate of change of H with respect to t at 3 p.m.

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 derivativeand 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, 0velocity and acceleration of the

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The table below shows the position S, of a dust particle as it moves over the course of an hour. The time t is given in minutes and the position is in feet.
[TABLE]
Use your calculator's regression feature, to find the cubic model that gives the position S in terms of the minutes t. Round to

I need to determine how fast a shadow is moving up a wall. Given the heigth of the wall the height if the object that cast the shadow. The length of the wire the object moves on, and the height of the light that casts the shadow. I have worked out the
first sections in an Excel 2000 spreadsheet but I need a push in the right di

The velocity v of a rocket attempting to escape from the earth's gravitational field is given by:
(v)(dv/dr) = -g(R^2/r^2)
Where:
r is its distance from the centre of the earth and
R is the mean radius of the earth
Find a formula for V(r) and determine the minimum launch velocity V0 in order that the rocket escap

A projectile is launched from a platform 20 feet high with an initial velocity of 112 feet per second, The height h of the projectile at t seconds after launch is given h= - 16t^2 + 112t +20 feet.
a. How many seconds after launch does the projectile attain maximum height?
b. What is the maximum height?

If a rock is thrown into the air on small planet with a velocity of 25 meters/second, its height in meters after t seconds is given by V = 25t ? 4.9t2. Find the velocity of the rock when t=3
A particle moves along a straight line and its position at time t is given by s(t) = 2t3 ? 27t2 + 108t where s is measured in meters and t