Question

A record club has found that the marginal profit,

Upper P prime left parenthesis x right parenthesisP′(x) ,

in cents, is given by

Upper P prime left parenthesis x right parenthesis equals negative 0.0008 x cubed plus 0.35 x squared plus 52.9 xP′(x)=−0.0008x^3+0.35x^2+52.9x

for

x less than or equals x≤400 ,

where x is the number of members currently enrolled in the club. Approximate the total profit when

240 members are enrolled by computing the sum

Summation from i equals 1 to 6 Upper P prime left parenthesis x Subscript i Baseline right parenthesis Upper Delta x∑i=16P′xiΔx

with

Upper Delta x equals 40Δx=40.

Answer 1