Calc help please!!!!!?
Question: Suppose hardware store customers are willing to buy T(p) boxes of nails at P dollars per box, where
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
where (0 < p < or equal 11)
Find:
a.) Average rate of change in demand for a change in price from $5 to $8
b.) Find the instantaneous rate of change in demand when the price is $5
Answers: Your original problem:
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
where (0 < p < or equal 11)
Find:
a.) Average rate of change in demand for a change in price from $5 to $8
find the change in Y over change in X for : T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
(T(8) - T(5)) / (8 - 5)
This yields:
(77.76 - 153.75) / 3
which equals:
-25.33
b.) Find the instantaneous rate of change in demand when the price is $5
This requires taking the first derivative:
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
T'(P) = 0.24p^3 - 3.75p^2 + 13p - 18
Evaluated at T'(5) = -16.75
Hope that helps...
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
where (0 < p < or equal 11)
Find:
a.) Average rate of change in demand for a change in price from $5 to $8
b.) Find the instantaneous rate of change in demand when the price is $5
Answers: Your original problem:
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
where (0 < p < or equal 11)
Find:
a.) Average rate of change in demand for a change in price from $5 to $8
find the change in Y over change in X for : T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
(T(8) - T(5)) / (8 - 5)
This yields:
(77.76 - 153.75) / 3
which equals:
-25.33
b.) Find the instantaneous rate of change in demand when the price is $5
This requires taking the first derivative:
T(P) = .06p^4 - 1.25p^3 + 6.5p^2 - 18p + 200
T'(P) = 0.24p^3 - 3.75p^2 + 13p - 18
Evaluated at T'(5) = -16.75
Hope that helps...
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