Paul Kersey
New member
- Joined
- Jun 6, 2012
- Messages
- 2
Hi, I'm taking a business analysis class and we just started doing derivatives. I haven't had any calculus classes before but I'm doing all right. Not sure about this word problem however.
The yield, Y, of an apple orchard (measured in bushels of apples per acre) is a function of the amount "x" of fertilizer in pounds used per acre. Suppose:
Y= f(x) = 320+140x-10x²
(a) What is the yield if 5 pounds of fertilizer are used per acre?
To solve this I simply plugged 5 into the x values. Y=320+700-250 simplified to Y=770. That is to say the yield is 770 bushels of apples per acre if five pounds of fertilizer are used per acre.
(b) Find f'(5). Give units with your answer and interpret it in terms of apples and fertilizer.
To solve this I took the derivative of 320+140x-10x², plugging 5 in for x.
f'(5)=140-10x(2)
f'(5)=140-20x
f'(5)=140-20(5)
f'(5)= 40
Ok, so I have f'(5)=40. I am not sure what this number means. I do not know how it relates in terms of apples and fertilizer. I hope I did everything right so far. Thanks for any help.
The yield, Y, of an apple orchard (measured in bushels of apples per acre) is a function of the amount "x" of fertilizer in pounds used per acre. Suppose:
Y= f(x) = 320+140x-10x²
(a) What is the yield if 5 pounds of fertilizer are used per acre?
To solve this I simply plugged 5 into the x values. Y=320+700-250 simplified to Y=770. That is to say the yield is 770 bushels of apples per acre if five pounds of fertilizer are used per acre.
(b) Find f'(5). Give units with your answer and interpret it in terms of apples and fertilizer.
To solve this I took the derivative of 320+140x-10x², plugging 5 in for x.
f'(5)=140-10x(2)
f'(5)=140-20x
f'(5)=140-20(5)
f'(5)= 40
Ok, so I have f'(5)=40. I am not sure what this number means. I do not know how it relates in terms of apples and fertilizer. I hope I did everything right so far. Thanks for any help.