Suppose that $f$ is a function given as $f(x) = -5x + 7$. We will compute the derivative of $f$ at $x = 3$ as follows. First, we will compute and simplify the expression $f(3 + h)$. $f(3 + h) = $ Then we compute and simplify the difference quotient between $x = 3$ and $x = 3 + h$. $frac{f(3 + h) - f(3)}{h} = $ The derivative of the function at $x = 3$ is the limit of the difference quotient as $h$ approaches zero. $f'(3) = lim_{h o 0} frac{f(3 + h) - f(3)}{h} = $
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Step 1:** Substitute x = 3 into the function f(x) = 5x + 7 to find f(3): f(3) = 5(3) + 7 f(3) = 15 + 7 f(3) = 22 ** Show more…
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Suppose that f is a function given as f(x) follows. We will compute the derivative of f at x = 5 as follows. First, we compute and simplify the expression f(5 + h). f(5 + h) Then we compute and simplify the difference quotient, between x = 5 and x = 5 + h. (f(5 + h) - f(5)) / h The derivative of the function at x is the limit of the difference quotient as h approaches zero. f'(5) = lim h->0 (f(5 + h) - f(5)) / h
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