How do you find the average rate of change of y with respect to x on the interval [1,4], where y=x2+x+1?

Question

Marin Lowe · Accepted Answer

The average rate of change of y over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
To calculate the average rate of change between the 2 points use.

\frac{f (b) - f (a)}{b - a}

f (4) = 4^{2} + 4 + 1 = 21

and

f (1) = 1^{2} + 1 + 1 = 3

The average rate of change between (1 ,3) and (4 ,21) is

\frac{21 - 3}{4 - 1} = \frac{18}{3} = 6

This means that the average of all the slopes of lines tangent to the graph of y between (1 ,3) and (4 ,21) is 6.

xmzdenisemst0 · Accepted Answer

Find the average rate of change of f(x)=x2+x+1 on the interval [1,4].The average rate of change of f(x) on the interval [a,b] is f(b)−f(a)b−aWe have that a=1, b=4, f(x)=x2+x+1.Thus, f(b)−f(a)b−a=1+(4)+(4)2−(1+1+12)4−(1)=6Answer: 6

How do you find the average rate of

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