AP Calculus AB / Differentiation: Definition and Basic Derivative Rules / Question No. 13

13. If \( f(x) = -x^2 + x \), then which of the following expressions represents \( f'(x) \) ?

\(\lim\limits_{h \to 0} \frac{(-x^2 + x + h) - (-x^2 + x)}{h}\)

\(\lim\limits_{h \to x} \frac{(-x^2 + x + h) - (-x^2 + x)}{h}\)

\(\frac{[-(x + h)^2 + (x + h)] - (-x^2 + x)}{h}\)

\(\lim\limits_{h \to 0} \frac{[-(x + h)^2 + (x + h)] - (-x^2 + x)}{h}\)

Answer is: option4 - \(\lim\limits_{h \to 0} \frac{[-(x + h)^2 + (x + h)] - (-x^2 + x)}{h}\)

Solution:

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Home Practice Questions AP Calculus AB Differentiation: Definition and Basic Derivative Rules Question No. 13