Question

Need some help with this question. Cannot figure it out. Thank you

Answer 1

We are asked to find whether the function is increasing or decreasing over the interval [2, 7]

Let us find the derivative of the given function,

If the derivative is greater than 0 then the function is increasing.

If the derivative is less than 0 then the function is decreasing.

`\begin{gathered} f(x)=-2x+4 \\ f^(\prime)(x)=-2x^(1-1)+0 \\ f^(\prime)(x)=-2x^0 \\ f^(\prime)(x)=-2 \end{gathered}`

As you can see, the derivative is less than 0, which means that the function is decreasing.

The rate of change of the function is given by

`m=(y_2-y_1)/(x_2-x_1)`

We need to select any two points from the interval [2, 7]

`\begin{gathered} f(2)=-2(2)+4=-4+4=0 \\ f(7)=-2(7)+4=-14+4=-10 \end{gathered}`

So, the two points are (2, 0) and (7, -10)

`m=(y_2-y_1)/(x_2-x_1)=(-10-0)/(7-2)=(-10)/(5)=-2`

Therefore, the rate of change of function is -2