The profit from manufacturing x items is given by P(x)= -0.5x^2+46x-10. Find change in P [20,21].

Question

I found the P'(x) and plugged in 20 to x and got $26, but the answer is supposed to be $25.50. I don't know what I did wrong here. Please help!!

Answer 1

I think they just want the average rate of change, so
P(21) = -.5(21)^2 + 46(21 - 10 = 735.5
P(20) = 710

average rate of change = (735.5-710)/(21-20) = 25.5

"I found the P'(x) and plugged in 20 to x and got $26" ---> you found the instantaneous
rate of change when x = 20

Answer 2

Thank you very much!