the above is the graph of the derivative f (x). how many critical points does the original function f(x) have?
the above is the graph of the derivative f (x). how many critical points does the original function f(x) have?
Answer
Explanation:
Step1: Recall critical - point definition
Critical points of $f(x)$ occur where $f^{\prime}(x)=0$ or $f^{\prime}(x)$ is undefined.
Step2: Analyze the graph of $f^{\prime}(x)$
The graph of $f^{\prime}(x)$ is a continuous curve. We look for the $x$ - values where $y = f^{\prime}(x)=0$. The graph of $f^{\prime}(x)$ crosses the $x$ - axis at three distinct points.
Answer:
3