Question

the table below shows the function of f determine the value of f(3) that will lead to an average rate of change of 19 over the interval [3, 5]​

Answer 1

`f(3) = - 25`

Step-by-step explanation

We want to determine the value of f(3) that will lead to an average rate of change of 19 over the interval [3, 5].

The average rate of change of f(x) over the interval [a,b]:

`= (f(b) - f(a))/(b - a)`

If the average rate of change over the interval [3, 5] is 19, then;

`(f(5) - f(3))/(5 - 3) = 19`

From the to table f(5)=13

`(13 - f(3))/(2) = 19`

`13 - f(3) = 19 * 2`

`13 - f(3) = 38`

`- f(3) = 38 - 13`

`- f(3) = 25`

`f(3) = - 25`