A curve has equation $y = \frac{k}{x}$ $y=k/x$ . Given that the gradient of the curve is $- 3$ $-3$ when $x = 2$ $x=2$ . Find the value of constant $k .$ $k.$ ?

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A curve has equation $y = \frac{k}{x}$ $y=k/x$ . Given that the gradient of the curve is $- 3$ $-3$ when $x = 2$ $x=2$ . Find the value of constant $k .$ $k.$ ?

A curve has equation $y = \frac{k}{x}$ $y=k/x$ . Given that the gradient of the curve is $- 3$ $-3$ when $x = 2$ $x=2$ . Find the value of constant $k .$ $k.$

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Answer 1 · 2018-01-21T13:50:44

$k = 12$ $k=12$

Explanation:

$∙ x m_{tangent} = \frac{d y}{d x} at x = 2$ $•color(white)(x)m_(color(red)"tangent")=dy/dx" at x = 2"$

$y = \frac{k}{x} = k x^{- 1}$ $y=k/x=kx^-1$

$\Rightarrow \frac{d y}{d x} = - k x^{- 2} = - \frac{k}{x^{2}}$ $rArrdy/dx=-kx^-2=-k/x^2$

$- \frac{k}{x^{2}} = - 3 when x = 2$ $-k/x^2=-3" when "x=2$

$\Rightarrow - k = - 3 \times 4 = - 12 \Rightarrow k = 12$ $rArr-k=-3xx4=-12rArrk=12$

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A curve has equation $y = \frac{k}{x}$ $y=k/x$ . Given that the gradient of the curve is $- 3$ $-3$ when $x = 2$ $x=2$ . Find the value of constant $k .$ $k.$ ?

A curve has equation $y = \frac{k}{x}$ $y=k/x$ . Given that the gradient of the curve is $- 3$ $-3$ when $x = 2$ $x=2$ . Find the value of constant $k .$ $k.$

1 Answer

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A curve has equation y=kxy=k/x. Given that the gradient of the curve is −3-3 when x=2x=2. Find the value of constant k.k. ?

A curve has equation y=kxy=k/x. Given that the gradient of the curve is −3-3 when x=2x=2. Find the value of constant k.k.

1 Answer

Explanation:

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