The profit from manufacturing x items is given by P(x)= -0.5x^2+46x-10. Find change in P [20,21].
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!!
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
Thank you very much!
To find the change in profit over the interval [20, 21], we need to calculate the difference in profit between these two values of x, which we'll call ΔP.
First, let's find the profit at x = 20 by substituting it into the equation P(x):
P(20) = -0.5(20)^2 + 46(20) - 10
= -0.5(400) + 920 - 10
= -200 + 920 - 10
= 710
Now, let's find the profit at x = 21:
P(21) = -0.5(21)^2 + 46(21) - 10
= -0.5(441) + 966 - 10
= -220.5 + 966 - 10
= 735.5
The change in profit (ΔP) is then calculated as:
ΔP = P(21) - P(20)
= 735.5 - 710
= 25.5
Based on these calculations, the correct change in profit between 20 and 21 items is $25.50.
It seems that you made a minor calculation error when finding the profit at x = 21. Please double-check your calculations to ensure accurate results.