Practice Definition Of The Derivative (limit Definition) (1.2)

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6 sample questions

Question 1.
Calculate the derivative of f(x) = 3x + 5 using the limit definition.
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Start by applying the limit definition with h approaching 0.
Question 2.
What does the derivative of a constant function (e.g., f(x) = 7) equal?
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Recall the nature of constant functions.
3Question 3.
What is the definition of the derivative?
- The slope of a secant line.
- The slope of a tangent line.
- The area under a curve.
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Think about how we calculate the slope at a point.
4Question 4.
True or False: The derivative of a constant function is zero.
- True
- False
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Consider the definition of a constant function.
Question 5.
Given a function f(x) = 2x^2 + 3x - 5, find the derivative using the limit definition and confirm with shortcut methods.
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Remember to simplify the limit carefully.
Question 6.
Analyze the function f(x) = e^x and find its derivative by using the limit definition.
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Recall that e^x behaves particularly well in limits.

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