Find the derivative of the function using the definition of derivative. f(x) = px + b f'(x) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)
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Given function: \( f(x) = px + b \) Using the definition of derivative: \( f'(x) = \lim_{{h \to 0}} \frac{f(x+h) - f(x)}{h} \) Substitute the function into the formula: \( f'(x) = \lim_{{h \to 0}} \frac{(p(x+h) + b) - (px + b)}{h} \) Simplify the expression: Show more…
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