How to maximize the area under -log(x) curve?

I'm trying to get the x and y coordinates for which the area under the curve: y=-15.7log(x)+154.94 is maximum. I would like to compute this in R or Python. Can someone please help me to find it?

Background: I have data points of sales (y) vs prices (x). I tried fitting a log curve in R: lm(formula = y ~ log(x)) which gave me the above equation. I'm trying to increase the revenue which is the product of sales and prices. Hence the rectangular area under the curve should be maximized.

Solution

R solution

# objective function should be minimized
NegArea <- function (x) x * (15.7 * log(x) - 154.94)
# sketch this function: there is a minimum
curve(NegArea, from = 0, to = 10000)
# use optimize()
optimize(NegArea, c(4000, 8000))

Analytical solution

First derivative is:

15.7 + 15.7 * log(x) - 154.94

Set it to zero and solve it:

x = 7106.675

This agrees with R result.