## Related questions with answers

Question

Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(t)=t^2-7, [3,3.1]

Solutions

VerifiedSolution A

Solution B

Answered 9 months ago

Step 1

1 of 6The **average rate of change** of a function $f(x)$ over the interval $[x_1,x_2]$ is given by

$\text{ave. rate of change}=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}.$

Answered 9 months ago

Step 1

1 of 2average rate of change = $\dfrac{f(3.1)-f(3)}{3.1-3}=\dfrac{3.1^2-7-3^2+7}{0.1}=6.1$

Now, $f'(t)=2t$

So $f'(3)=6$

while $f'(3.1)=6.2$

So $f'(3)\text{\textless}\text{ average rate of change }\text{\textless} f'(3.1)$

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