Question

Determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5. Justify your answer.

Answer 1

Explanation:

Given

The function is
`f(x)=x+4`

for
`x_2>x_1`, we will check the values of
`f(x_1)` and
`f(x_2)`

Take 3 and 4

`f(4)=4+4\\f(4)=8`

Similarly,

`f(3)=3+4\\f(3)=7`

Thus,
`f(4)>f(3)`

Also,
`f'(x)` is 1 i.e. a constant value. So, the function is increasing linearly for the given interval.