Increasing Functions: Explained With Slopes And Derivatives

f(x) is increasing when

f’ > 0

A function, f(x), is said to be increasing if its values increase as the input variable x increases, or in other words, if its graph goes up as we move from left to right.

To determine whether a function, f(x), is increasing or not, we need to look at the slope or gradient of the function. If the slope is positive, then the function is increasing, while if the slope is negative, then the function is decreasing.

So, f(x) is increasing when its slope is positive or when the derivative of the function, f'(x), is positive. In other words, if for any value of x, f'(x) > 0, then the function is increasing.

Another way to determine if f(x) is increasing is to check whether the second derivative of the function, f”(x), is positive or not. If f”(x) > 0 for all x-values, then f(x) is increasing.

Therefore, we can conclude that a function, f(x), is increasing when the slope or gradient of the function is positive, or when the first derivative or second derivative of the function is positive.

More Answers: