Question

Solve any TEN of the following:
a) Find the gradient of the curve xy = 6 at pt (1, 6)​

Answer 1

Answer:

dy/dx= -6

Step-by-step explanation:

dy/dx = -6/x^2

at x= 1,

dy/dx = -6

Answer 2

The gradient of the curve xy = 6 at pt (1, 6) is - 6

Given :

The curve xy = 6

To find :

The gradient of the curve xy = 6 at pt (1, 6)

Solution :

Step 1 of 3 :

Write down the given equation of the curve

Here the given equation of the curve is xy = 6

Step 2 of 3 :

Find dy/dx

$\displaystyle \sf{ xy = 6 }$

$\displaystyle \sf{ \implies y = \frac{6}{x} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx}= - \frac{6}{ {x}^{2} } }$

Step 3 of 3 :

Find gradient of the curve

The gradient of the curve xy = 6 at pt (1, 6)

$\displaystyle \sf{ = \frac{dy}{dx} \bigg| _{(1,6)} }$

$\displaystyle \sf{ = - \frac{6}{ {1}^{2} } }$

$\displaystyle \sf{ = - 6 }$