Question

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

Answer 1

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

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

$f(x)=-\dfrac{1}{2}x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

At x = 0, the value of x is

$f(0)=-\dfrac{1}{2}\times 0+2=2$

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

$f(4)=-\dfrac{1}{2}\times4+2=-2+2=0.$

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

$A_v=\dfrac{f(4)-f(0)}{4-0}=\dfrac{0-2}{4}=-\dfrac{2}{4}=-\dfrac{1}{2}.$

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

Answer 2

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.