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

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 2

Answer: The required average rate of change from x = 0 to x = 4 is
`-(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)=-(1)/(2)x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

At x = 0, the value of x is

`f(0)=-(1)/(2)* 0+2=2`

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

`f(4)=-(1)/(2)*4+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=(f(4)-f(0))/(4-0)=(0-2)/(4)=-(2)/(4)=-(1)/(2).`

Thus, the required average rate of change from x = 0 to x = 4 is
`-(1)/(2).`