Answer:
a. -3
b. -3
Step-by-step explanation:
Fill in the function arguments and simplify.
a.
[tex]\dfrac{f(x)-f(a)}{x-a}=\dfrac{(-3x+9)-(-3a+9)}{x-a}=\dfrac{-3x+9+3a-9}{x-a}\\\\=\dfrac{-3(x-a)}{(x-a)}=-3[/tex]
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b.
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(-3(x+h)+9)-(-3x+9)}{h}=\dfrac{-3x-3h+9+3x-9}{h}\\\\=\dfrac{-3h}{h}=-3[/tex]
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Comment on questions of this type
Perhaps the point of this exercise is to help you understand that the average slope computed by the first expression approaches the instantaneous slope computed by the second expression. This happens when a approaches x and when h approaches zero.
In this problem, where the function is a straight line, the slope is a constant (-3), so the average slope and the instantaneous slope are the same everywhere (for all values of x, a, h).
