Question

Suppose that the function graphed below is f'(x), the derivative of f(x). Find the locations of all relative extrema of f(x).

Answer 1

Final Answer:
The locations of all relative extrema of
`\( f(x) \)` can be determined by identifying the points where f'(x) = 0 or f'(x) is undefined.

Step-by-step explanation:

To find the relative extrema of f(x), we look for critical points where the derivative f'(x) is either equal to zero or undefined.

Firstly, set f'(x) = 0 and solve for ( x ) to find the critical points. These are the values of ( x ) where the function f(x) may have relative extrema.

Secondly, check for points where f'(x) is undefined. These points may also indicate locations of relative extrema.

In summary, the relative extrema of f(x) are found at the critical points where f'(x) = 0 or is undefined. These points correspond to places where the slope of the function is either zero or undefined, suggesting possible peaks, troughs, or points of inflection. By analyzing these critical points and considering the behavior of f(x) in the vicinity of these points, one can determine whether they are maxima, minima, or points of inflection in the graph of f(x).