Question

let f be a function such that f(2) = -4 and f(2) = 4. let g be the function g(x) = 2x². let g be a function defined as g(x) = f(x)/g(x). g(2) =

Explanation:

Step1: Apply the quotient rule

The quotient rule states that if \(G(x)=\frac{f(x)}{g(x)}\), then \(G'(x)=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\).

Step2: Find \(g(2)\) and \(g'(x)\)

Given \(g(x) = 2x^2\), then \(g'(x)=4x\). So \(g(2)=2\times2^2 = 8\) and \(g'(2)=4\times2 = 8\).

Step3: Substitute into the quotient rule formula

We know \(f(2)=- 4\), \(f'(2)=4\), \(g(2)=8\), \(g'(2)=8\).

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Answer:

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