Let the price function be p = 15E ^ - X / 3 (x is the output) I need help

Let the price function be p = 15E ^ - X / 3 (x is the output) I need help

Income y = PX = (15E ^ (- X / 3)) x
y'=-5e^(-x/3)x+15e^(-x/3)
When y '= 0, y has extremum
-5e^(-x/3)x+15e^(-x/3)=0
x=3
Single increasing interval: y '> 0 - 5E ^ (- X / 3) x + 15E ^ (- X / 3) > 0 x

A shopping mall operates a batch of small commodities with a purchase price of 2 yuan. According to the experience, it is speculated that the daily sales unit price x yuan of this commodity is between the profit P
P = - 2x ^ 2 + 28x-18, then what is the daily sales unit price to make a daily profit of 30 yuan?

30 = - 2x ^ 2 + 28x-18, the solution is X1 = 2, X2 = 12; when X1 = 2, rounding off x is 12, the profit is 30 yuan

When a shopping mall sells a commodity, its profit margin increases by 8 percentage points because the purchase price is 6.4% lower than the original purchase price?

Let the original purchase price be a yuan, and the original profit rate of this commodity be X. according to the equation, a (1 + x) − a (1 − 6.4%) a (1 − 6.4%) = x + 8%, and the solution is x = 17%

When a shopping mall sells a commodity, its profit margin increases by 8 percentage points because the purchase price is 6.4% lower than the original purchase price?

Let the original purchase price be a yuan, and the original profit rate of this commodity be X. according to the equation, a (1 + x) − a (1 − 6.4%) a (1 − 6.4%) = x + 8%, and the solution is x = 17%