Finding function for histogram to investigate on minimum, maximum and inflection points

Question

To investigate on the statistics of an image, I want to find out how to get all
1.) minima,
2.) maxima and
3.) inflection points
for the histogram of a specific image. I know how to extract the frequency for the pixel values in the image and how to plot the histogram as well as the function itself, but that is all. Thanks a lot in advance for your help!

see URL:Finding inflection points in R from smoothed data
see URL:http://r-datameister.blogspot.com/2013/08/changepoint-analysis-of-time-series.html

# get the frequenz, how often specific values occur and plot the head
image_freq <- freq(image)
head(image, n = 5)
     value count
[1,]   -56     1
[2,]   -55     4
[3,]   -53     3
[4,]   -52     5
[5,]   -51     4

# get variables for the x and y values and plot the graph
# FOR THIS GRAPH I WANT TO GET ALL MINIMA, MAXIMA AND INFLECTION POINTS
x_value <- image_freq[, 1]
y_value <- image_freq[, 2]
plot(x_value, y_value, type = 'l')