Question 1
Use the definition \( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \) to determine the derivative of \( f(x) = 2x^2 - 5x + 3 \) from first principles.
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Mathematical Methods Β· Unit 2 Β· Introduction to differential calculus Β· Rates of change and the concept of derivatives
Use the rule πβ²(π₯) = lim ββ0 π(π₯+β)βπ(π₯) β to determine the derivative of simple power functions and polynomial functions from first principles.
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Question 2
Use the first principles definition to determine $f'(2)$ for the function $f(x) = 3x^2 - 5$.
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Question 3
Use the definition of the derivative to determine $f'(2)$ for the function $f(x) = 3x^2 - 5x$.
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