Calculus, 2ADV C1 EO-Bank 11 MC v1

Two functions, \(f\) and \(g\), are continuous and differentiable for all \(x\in R\). It is given that \(f(-1)=7,\ g(-1)=5\) and \(f^{′}(-1)=-4,\ g^{′}(-1)=-2\).

The gradient of the graph \(y=\dfrac{f(x)}{g(x)}\) at the point where \(x=-1\) is

\(-\dfrac{6}{49}\)
\(\dfrac{6}{49}\)
\(\dfrac{6}{25}\)
\(-\dfrac{6}{25}\)

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\(D\)

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\(\text{Using the Quotient Rule when}\ \ x=-1:\)

\(\dfrac{d}{dx}\left(\dfrac{f(x)}{g(x)}\right)\)	\(=\dfrac{g(x)f^{′}(x)-f(x)g^{′}(x)}{g(x)^2}\)
	\(=\dfrac{g(-1)f^{′}(-1)-f(-1)g^{′}(-1)}{g(-1)^2}\)
	\(=\dfrac{5 \times -4-7 \times -2}{5^2}\)
	\(=-\dfrac{6}{25}\)

\(\Rightarrow D\)