Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

f(x) = 3x + 5

ok...i think you find the derivative first...? but i thought u had to find the critical points somehow... i am so lost! can someone show me how to do this problem? PLEASE! :)

Follow the rules. Derivative for the slope, which in this case is always positive. The second derivative is zero.

There are no critical points. and there are no intervals where the function is decreasing.

To determine the intervals where the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Step 1: Find the derivative of the function, f(x) = 3x + 5.
The derivative will give us information about the slope of the function at different points. In this case, since we only have a linear function, the derivative will be a constant value.

The derivative of f(x) = 3x + 5 is simply the coefficient of x, which is 3. So, f'(x) = 3.

Step 2: Analyze the sign of the derivative.
To find the intervals where the function is increasing or decreasing, we need to determine where the derivative is positive (increasing function) or negative (decreasing function).

Since the derivative is a constant value of 3, it's always positive. This means the function f(x) = 3x + 5 is always increasing.

Step 3: Determine the intervals.
Based on the information above, we can conclude that the function f(x) = 3x + 5 is increasing on the entire number line. There are no intervals where it is decreasing.

In summary, the function f(x) = 3x + 5 is increasing on the entire number line.