f(x) is increasing -> f'(x) is
positive
positive.
If a function f(x) is increasing, it means that as x increases, the value of f(x) also increases. Mathematically, we can define an increasing function as:
if x1 < x2, then f(x1) < f(x2) Now, we know that the derivative of a function f'(x) represents the rate of change of the function with respect to x. So, if a function is increasing, it means that its rate of change is positive. This can be expressed mathematically as: if f(x) is increasing, then f'(x) > 0
Therefore, we can conclude that if f(x) is increasing, then f'(x) is positive.
More Answers:
the Significance of Positive to Negative Slope Changes in Math: Critical Points and Inflection PointsMastering Calculus: Identifying Critical Points for Optimal Solutions
the Relationship Between the Function and Derivative: The Impact of Decreasing Functions
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded