Explanation:
F'(x) = f(x + h)² - 5(x + h) + 3 - (x² - 5x + 3)
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h
F'(x) = x² + 2xh + h² - 5x - 5h + 3 - x² + 5x - 3
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h
F'(x) = 2xh + h² - 5h
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h
F'(x) = h(2x + h - 5)
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h
F'(x) = 2x + h - 5
Lim
h---0
= 2x + 0 - 5
= 2x - 5