Increasing F'(X): How It Affects Steepness And Rate Of Change In F(X)

When f ‘(x) is increasing, f(x) is

concave up

When f ‘(x) is increasing, it means that the derivative of f(x) is itself increasing, i.e., the rate at which f(x) changes is increasing. This implies that f(x) is becoming steeper i.e., the slope of the tangent line to the graph of f(x) is increasing as we move from left to right along the x-axis.

In other words, the values of f(x) are increasing at an increasing rate as x increases. This means that f(x) is getting larger at an increasing rate as x increases.

To summarize, when f ‘(x) is increasing, f(x) is becoming steeper, and the values of f(x) are increasing at an increasing rate as x gets larger.

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