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Question
Equation: y=.27X^3-6.31X^2+29.87X+34.7
with the relationship between x given as gross domestic product per capita income in thousands of dollars and y given as units of smoke in cities.
Question: Find derivitives where
x=2 Derivitive=17.87
x=3 Derivitive=9.30
x=5 Derivitive=-2.98
x=6 Derivitive=-6.69
Based on these derivitive values, does environmental quality deteriorate with economic growth using this model?
I am not exactly sure what the derivitives mean in this context. Could you help me out?
The derivative of x^3=3x^2, x^2=2x, etc. This is what I understand to be the derivative, and what I get for x=2,3,5,6 is different than what's given. I get dy/dx at x=2,3,5 and 6 to be respectively 58.35, 75.02, 113.22, and 145.75.
From the information you have given and the definition you have given for derivatives, it would seem that there would be growth in years 2 and 3, but then decrease in years 5 and 6.
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