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The graph of cube root function m is shown: Compare the average rate of change of m to the average rate of change of h(x) = V4r over the interval + = 0 tox = 4 Round your answer to the nearest hundredth:
The average rate of change of m is about
times the average rate of change of h over the interval x = 0 tox= [=

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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.$$h(x)=x^{3}-\frac{1}{2} e^{x}$$

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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.$$h(x)=x^{3}-\frac{1}{2} e^{x}, \quad[0,2]$$

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Find the average rate of change of the function f over the given interval.$$f(x)=-\sqrt{x^{4}-x^{3}+2 x^{2}-x+4} \text { from } x=0 \text { to } x=3$$

Transcript

This problem says the graph of cube root function m is shown, and we’re asked to compare the average rate of change of m to the average rate of change of h of x equals cube root of 4x over the interval from 0 to 4, and round our answer to the nearest hundredth. And the blank we’re asked to fill in is the average rate of change of m is about blank times the average rate of change of h over the interval 0 to 4. So to be able to figure this out we need to know the formula for rate of change or average rate of change, which is f of b minus f of a divided by b minus a. And in this case our a value is our 0 and our b value is 4. So looking at our m function for the graph on the left, if we want to evaluate f of b and f of a, we’ll look at the x values of 0 and 4 and look at their outputs. So if our b value was 4, we want f of 4. f of 4 looks to evaluate at 2 for that y value because that’s the point 4, 2. So that would be 2 minus f of a, where f of a would be f of 0. And at 0 we also have the y value 0 at the origin, so that’s 2 minus 0 over b minus a, which is 4 minus 0. That gives us 2 over 4, and that simplifies to 0 .5 or 1 half. So that’s our average rate of change for m. Now to find the average rate of change for h of x, we don’t have a graph but we’re given the function so we can evaluate. First for h of 4, that gives us cube root of 4 times 4. That is going to give us the cube root of 16. And when we evaluate that in the…