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Exercise 1

Avg difficulty 2.5

Find the first derivative formula for each of the following functions twice: first by evaluating lim⁡h→0f(x+h)−f(x)h\lim\limits_{h\to0}\frac{\fe{f}{x+h}-\fe{f}{x}}{h} and then by evaluating lim⁡t→xf(t)−f(x)t−x\lim\limits_{t\to x}\frac{\fe{f}{t}-\fe{f}{x}}{t-x}.

f(x)=x2\fe{f}{x}=x^2

Simonds, Calculus Lab Manual, §3.5 Supplement, Exercise 1

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Adapted from Calculus Lab Manual © 2012–2016 Portland Community College. Licensed under CC BY-SA 4.0. Source: Calculus Lab Manual. Imported at revision 3060f8e.