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

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

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

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

S represents weekly sales of a product. What can be said of S' and S'' for each of the following?
(a) the rate of change of sales is increasing
(b) sales are increasing at a slower rate
(c) the rate of change of sales is constant
(d) sales are steady
(e) sales are declining, but at a slower rate
(f) sal

Please show all the steps to calculate the answers to the attached questions about using the chain rule on an American population function and a demand function for desk lamp prices.

#1 Write an equation of the line tangent to the curve y=f(x) at the given point P on the curve. Express the answer in the form ax+by=c.
1)y=3x^2-4; P(1,-1)
2)y=2x-1/x; P(0.5,-1)
#2 Give the position function x=f(t) of a particle moving in a horizontal straight line. Find its location x when its velocity v is zero.
1)x=-1

The parabola y = (x^2) + 3 has two tangents which pass through the point (0, -2). One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ?
If a ball is thrown vertically upward from the roof of 64ft foot building with a velocity of 96 ft/sec, its height after t seconds

One end of a long wire under tension is moved up and down sending a wave along it. Assume the wire lies along an x axis with the moving end at the origin. The equation giving displacement y, in meters, of points on the wave is:
(1) y= (.06 m) sin (5 x - 25 t)
a. From given constants, calculate the value and units of the quan