Question

Given the function f(x) = x² - 2x, which of the following is the correct limit definition of f′(2) ?

A. lim(h→0)h² - h - 4/h

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B. lim(h→0) (2 + h)² - 4/h

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C. lim(h→0) (2 + h)² - 2h - 4/h

D. lim(h→0) (2 + h)² + 4/h

Answer 1

The correct limit definition of f′(2) for the given function is option C. lim(h→0) (2 + h)² - 2h - 4/h.

Step-by-step explanation:

The correct limit definition of f′(2) for the function f(x) = x² - 2x is option C. lim(h→0) (2 + h)² - 2h - 4/h.

To find the limit definition of the derivative, we need to use the limit definition of the derivative formula: f′(x) = lim(h→0) (f(x + h) - f(x))/h. Substitute x = 2 into the formula to get f′(2) = lim(h→0) (f(2 + h) - f(2))/h.

Substitute the given function f(x) = x² - 2x into the formula and simplify the expression to get the correct answer.