positive derivative means the
rate of change of a function is increasing
rate of change of a function is increasing. In mathematics, the derivative of a function measures the steepness of the function at a given point and gives us information about how the function is changing.
If the derivative of a function is positive, it means that as we move along the x-axis from left to right, the y-values of the function are increasing. In other words, the function is getting steeper and its rate of change is becoming more positive.
Graphically, a positive derivative means that the slope of the tangent line to the curve at any point is positive. This indicates that the function is trending upwards and getting larger as the independent variable increases.
For example, let’s consider the function f(x) = x^2. The derivative of this function is f'(x) = 2x. This derivative is positive for all x values greater than 0. This means that as we move along the x-axis to the right, the y-values of the function are increasing. The slope of the tangent line is positive, indicating that the function is getting steeper and its rate of change is increasing.
In summary, a positive derivative indicates that a function is increasing, both in terms of its slope and its rate of change.
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