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Find the derivative of y = 2x2 − x + 3 from first principles.
Mathematics
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Answer
4x - 1
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| Point | x | y |
|---|---|---|
| y-intercept | 0 | 3 |
| Minimum | 0.25 | 2.88 |
Step-by-step solution
5 stepsTo find the derivative of from first principles, we use the definition:
Identify and .
Given .
Substitute into to find :Calculate .
Substitute into the first principles formula.
Factor out from the numerator and simplify.
Since but , we can cancel :
Evaluate the limit by substituting .
The derivative of is .
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