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Chapter 2: Problem 64
Refer to the function \(f=\\{(2,3),(9,7),(3,4),(-1,6)\\} .\) Determine \(f(2)\).
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A car traveling \(60 \mathrm{mph}(88 \mathrm{ft} / \mathrm{sec})\) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance \(d(t)\) (in ft) that the car travels \(t\) seconds after the brakes are applied is given by \(d(t)=-4.84 t^{2}+88 t,\) where \(0 \leq t \leq 9.09 .\) (See Example 5) a. Find the difference quotient \(\frac{d(t+h)-d(t)}{h}\). Use the difference quotient to determine the average rate of speed on the following intervals for \(t\) : b. [0,2]\(\quad(\) Hint \(: t=0\) and \(h=2)\) c. [2,4]\(\quad(\) Hint \(: t=2\) and \(h=2)\) d. [4,6]\(\quad(\) Hint \(: t=4\) and \(h=2)\) e. [6,8]\(\quad(\) Hint \(: t=6\) and \(h=2)\)
Evaluate the step function defined by \(f(x)=[x]\) for the given values of \(x\). $$ f(0.5) $$
A car accelerates from 0 to \(60 \mathrm{mph}(88 \mathrm{ft} / \mathrm{sec})\) in \(8.8 \mathrm{sec} .\) The distance \(d(t)\) (in \(\mathrm{ft}\) ) that the car travels \(t\) seconds after motion begins is given by \(d(t)=5 t^{2},\) where \(0 \leq t \leq 8.8\) a. Find the difference quotient \(\frac{d(t+h)-d(t)}{h}\). Use the difference quotient to determine the average rate of speed on the following intervals for \(t:\) b. [0,2] c. [2,4] d. [4,6] e. [6,8]
The amount of \(\mathrm{CO}_{2}\) emitted per year \(A(x)\) (in tons) for a vehicle that burns \(x\) miles per gallon of gas, can be approximated by \(A(x)=0.0092 x^{2}-0.805 x+21.9 .\) (Source: U.S. Department of Energy, http://energy.gov) a. Determine the difference quotient. \(\frac{A(x+h)-A(x)}{h}\) b. Evaluate the difference quotient on the interval \([20,25],\) and interpret its meaning in the context of this problem. c. Evaluate the difference quotient on the interval \([35,40],\) and interpret its meaning in the context of this problem.
Suppose that the average rate of change of a continuous function between any two points to the left of \(x=a\) is positive, and the average rate of change of the function between any two points to the right of \(x=a\) is negative. Does the function have a relative minimum or maximum at \(a\) ?
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