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Troyanec [42]
3 years ago
10

Please helppp with this math question <333

Mathematics
1 answer:
Naya [18.7K]3 years ago
5 0

Answer:

The average rate of change of the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1 is -1

Step-by-step explanation:

We are given the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1

We need to find average rate of change.

The formula used to find average rate of change is : Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}

We have b=-1 and a=-11

Finding g(b) = g(-1)

g(x)=x^2+10x+18\\Putting \ x=-1\\g(-1)=(-1)^2+10(-1)+18\\g(-1)=1-10+18\\g(-1)=9

Finding g(a) = g(-11)

g(x)=x^2+10x+18\\Putting \ x=-11\\g(-11)=(-11)^2+10(-11)+18\\g(-1)=121-110+18\\g(-1)=29

Finding average rate of change

Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{9-29}{-1-(-11)}\\Average \ rate \ of \ change=\frac{-10}{-1+11}\\Average \ rate \ of \ change=\frac{-10}{10}\\Average \ rate \ of \ change=-1

So, the average rate of change of the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1 is -1

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