If \( f^{\prime}(x)>0 \) then \( f \) is increasing. True False

The statement "If \( f^{\prime}(x) > 0 \) then \( f \) is increasing" is **True**. ### Explanation: 1. **Definition of Derivative**: The derivative \( f^{\prime}(x) \) represents the rate of change of the function \( f(x) \) at a point \( x \). 2. **Positive Derivative**: If \( f^{\prime}(x) > 0 \), it means that the function \( f(x) \) is increasing at that point. This indicates that as \( x \) increases, \( f(x) \) also increases. 3. **Conclusion**: Therefore, if the derivative is positive over an interval, the function is increasing throughout that interval. Thus, the statement is true.