ANSWER
[tex]f(3) = - 25[/tex]
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]:
[tex] = \frac{f(b) - f(a)}{b - a} [/tex]
If the average rate of change over the interval [3, 5] is 19, then;
[tex]\frac{f(5) - f(3)}{5 - 3} = 19[/tex]
From the to table f(5)=13
[tex]\frac{13 - f(3)}{2} = 19[/tex]
[tex]13 - f(3) = 19 \times 2[/tex]
[tex]13 - f(3) = 38[/tex]
[tex] - f(3) = 38 - 13[/tex]
[tex] - f(3) = 25[/tex]
[tex]f(3) = - 25[/tex]
