current attempt in progress the figure below is a graph of the derivative $f$. for what values of $x$ does…

current attempt in progress the figure below is a graph of the derivative $f$. for what values of $x$ does $f$ have a local maximum? a local minimum? enter your answers, in increasing order, rounded to one decimal place. if there are less than three local maxima or minima, enter na in the remaining answer areas. the function $f$ has a local maximum when $x =$, $x =$, and $x =$. the function $f$ has a local minimum when $x =$, $x =$, and $x =$.

current attempt in progress the figure below is a graph of the derivative $f$. for what values of $x$ does $f$ have a local maximum? a local minimum? enter your answers, in increasing order, rounded to one decimal place. if there are less than three local maxima or minima, enter na in the remaining answer areas. the function $f$ has a local maximum when $x =$, $x =$, and $x =$. the function $f$ has a local minimum when $x =$, $x =$, and $x =$.

Answer

Explanation:

Step1: Recall the first - derivative test

If (f^{\prime}(x)) changes sign from positive to negative at a point (c), then (f(x)) has a local maximum at (x = c). If (f^{\prime}(x)) changes sign from negative to positive at a point (c), then (f(x)) has a local minimum at (x = c).

Step2: Analyze the sign - change of (f^{\prime}(x)) for local maxima

Looking at the graph of (f^{\prime}(x)), (f^{\prime}(x)) changes sign from positive to negative at (x = 5). There are no other such points in the given graph.

Step3: Analyze the sign - change of (f^{\prime}(x)) for local minima

(f^{\prime}(x)) changes sign from negative to positive at (x = 1) and (x = 3).

Answer:

The function (f) has a local maximum when (x = 5.0), (x=NA), (x = NA) The function (f) has a local minimum when (x = 1.0), (x = 3.0), (x=NA)