Given:
f(3)=10
The rate of change over the interval 3≤x≤5 is 15.
To find:
The value of f(5).
Solution:
The formula to find the slope or rate of change of function f over the interval [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Using this formula, the the rate of change of a function f over the interval 3≤x≤5 is
[tex]m=\dfrac{f(5)-f(3)}{5-3}[/tex]
Rate of change is 15 and f(3)=10. So,
[tex]15=\dfrac{f(5)-10}{2}[/tex]
Multiply both sides by 2.
[tex]30=f(5)-10[/tex]
[tex]30+10=f(5)[/tex]
[tex]40=f(5)[/tex]
Therefore, the value of f(5) is 40.
