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Find the average rate of change for the given function from x = 0 to x = 4. Graph of f of x equals negative one-half plus 2

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thndrbrd3
Unless you meant -1/2x+2 the top answer is correct. If you meant the other it is -1/2(d/dx(x+2), which results in -1/2(1) or -1/2.

Answer:  The required average rate of change from x = 0 to x = 4 is [tex]-\dfrac{1}{2}.[/tex]

Step-by-step explanation:  We are given to find the average rate of change for the following function from x = 0 to x = 4 :

[tex]f(x)=-\dfrac{1}{2}x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

At x = 0, the value of x is

[tex]f(0)=-\dfrac{1}{2}\times 0+2=2[/tex]

and at x = 4, the value of f(x) is

[tex]f(4)=-\dfrac{1}{2}\times4+2=-2+2=0.[/tex]

Therefore, the average rate of change of the function (i) from x = 0 to x = 4 i given by

[tex]A_v=\dfrac{f(4)-f(0)}{4-0}=\dfrac{0-2}{4}=-\dfrac{2}{4}=-\dfrac{1}{2}.[/tex]

Thus, the required average rate of change from x = 0 to x = 4 is [tex]-\dfrac{1}{2}.[/tex]

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