The profit P for a company is P=15,000+650x - x^2?

Question

Use differentials to approximate the change and the percent of change in profit as the production changes from x=91 to x=95 units.

Answer 1

if x=91
P= 15,000+650(91)-(91^2)
74150-8281 = 65869

if x=96
P= 15,000+650(96)-(96^2)
77400-9216 = 69184

so 5.03%

Answer 2

you differentiate

dP/dx= -2x+650

and if you think that dx is small, you can approximate

dP = (650-2x) dx

here x =91 dx = 95-91= 4

so dP = (650-2*91) *4 = 1872