Question

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Finding the average rate of change of a function given its...
Find the average rate of change of g (x) = -2x²-x from x = 1 to x = 6.
Simplify your answer as much as possible.
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18 08
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Answer 1

Mind you that the average rate of change is the gradient. Commonly we get it by using the formula that requires us to have also the y coordinates.

we can find them by plugging in the x-values in the function g(x)

x=1

`g(1)=-2(1^(2) )-1\\g(1)=-3\\\\g(6)=-2(6^(2))-1\\ g(6)=-73`

now we have the points (1,-3) and (6,-73)

`m=(y2-y1)/(x2-x1)`

that is the formula we will use

`=(-73-(-3))/(6-1) \\=(-70)/(5) \\=-14`