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$p(x)=4x+3q(x)=21 x_{2}+2 $ We have to find the rate of change of each function from $x=0$ to $x=1.$ Before starting the computations, let's remember the expression that gives us the average rate of change of a function $F(x)$ between $x=a$ and $x=b.$ $Rate of Change =Change inxChange iny =b−aF(b)−F(a) $ Using this formula, we can find the rate of change of each of the given functions.

Rate of Change $=b−aF(b)−F(a) $ | |
---|---|

$1−0p(1)−p(0) $ | $1−0q(1)−q(0) $ |

$1−04(1)+3−(4(0)+3) $ | $1−021 (1)_{2}+2−(21 (0)_{2}+2) $ |

$4$ | $0.5$ |

From the table above, we conclude that the function $p(x)$ has greater rate of change from $x=0$ to $x=1.$ We can also check it graphically.

b

$Rate of Change =Change inxChange iny =b−aF(b)−F(a) $ As in Part A, let's find the rate of change of each of the given functions from $x=2$ and $x=3.$

Rate of Change $=b−aF(b)−F(a) $ | |
---|---|

$3−2p(3)−p(2) $ | $3−2q(3)−q(2) $ |

$3−24(3)+3−(4(2)+3) $ | $3−221 (3)_{2}+2−(21 (2)_{2}+2) $ |

$4$ | $2.5$ |

From the table above, we conclude once more that the function $p(x)$ has a greater rate of change from $x=2$ to $x=3.$ We can also check it graphically.