The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.
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Correct Answer: Option A
Explanation:
When x = 2
y = 2(2)\(^3\) - 2(2)\(^2\)
-5(2) + 5
y = 16 - 8 - 10 + 5
y = 3
when x = 2.05
y = 2(2.105)\(^3\) - 2(2.05)\(^2\)
- 5(2.05) + 5
y = 17.23 - 8.405 - 10.25 + 5
y = 3.575 - 3
Difference = 3.575 - 3
= 0.58
When x = 2
y = 2(2)\(^3\) - 2(2)\(^2\)
-5(2) + 5
y = 16 - 8 - 10 + 5
y = 3
when x = 2.05
y = 2(2.105)\(^3\) - 2(2.05)\(^2\)
- 5(2.05) + 5
y = 17.23 - 8.405 - 10.25 + 5
y = 3.575 - 3
Difference = 3.575 - 3
= 0.58