The following graph shows the weight measurements of the ...



The following graph shows the weight measurements of the average infant from the time of birth

(t = 0) through age 2 (t = 24). By computing the slopes of the respective tangent lines, estimate the rate of change of the average infant's weight when t = 3 and when t = 18.

(Round your answers to one decimal place as needed.)

|t = 3      |1[pic] [pic][pic]lb/month |

|t = 18      |2[pic] [pic][pic]lb/month |

What is the average rate of change in the average infant's weight over the first year of life?

3[pic] [pic][pic]lb/month

[pic]

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2

Let f be defined as follows.

[pic][pic]

(a) Find the average rate of change of y with respect to x in the following intervals.

|from x = 6 to x = 7     |1[pic] |

| |[pic][pic] |

|from x = 6 to x = 6.5     |2[pic] |

| |[pic][pic] |

|from x = 6 to x = 6.1     |3[pic] |

| |[pic][pic] |

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

4[pic]

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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) = −0.1x2 − 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  |$ 1[pic] [pic][pic]per 1000 tents |

|between 4400 and 4410 tents |$ 2[pic] [pic][pic]per 1000 tents |

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

$ 3[pic] [pic][pic]per 1000 tents

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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.

[pic][pic]

Find the rate of population growth at t = 11 min.

1[pic] [pic][pic]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 − 16t2.

(a) What is the average velocity of the ball over the following time intervals?

|[4,5]     |1[pic] [pic][pic]ft/sec |

|[4,4.5]     |2[pic] [pic][pic]ft/sec |

|[4,4.1]     |3[pic] [pic][pic]ft/sec |

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

4[pic] [pic][pic]ft/sec

(c) What is the instantaneous velocity at time t = 8?

5[pic] [pic][pic]ft/sec

Is the ball rising or falling at this time? [pic]

[pic]rising [pic]falling    

[pic][pic]

(d) When will the ball hit the ground?

t = 7[pic] [pic][pic]sec

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