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

ANSWER

$f(3) = - 25$

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]:

$= \frac{f(b) - f(a)}{b - a}$

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

$\frac{f(5) - f(3)}{5 - 3} = 19$

From the to table f(5)=13

$\frac{13 - f(3)}{2} = 19$

$13 - f(3) = 19 \times 2$

$13 - f(3) = 38$

$- f(3) = 38 - 13$

$- f(3) = 25$

$f(3) = - 25$