Answer:
[tex]\fbox{Gradient of curve = -6}[/tex]
Step by step explanation:
Given:
Equation of curve ↦ xy = 6
Point ↦(1,6)
To find:
The gradient of curve = ?
Solution:
[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]
Taking log both the side,
[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]
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