Originally Posted by

**looi76** **Question:**

The equation of a curve is $\displaystyle y = \frac{6}{5 - 2x}$

(i) Calculate the gradient of the curve at the point where $\displaystyle x = 1$

(ii) A point with coordinates $\displaystyle (x, y)$ moves along the curve in such a way that the rate of increase of $\displaystyle y$ has a constant value of $\displaystyle 0.02$ units per second. Find the rate of increase of $\displaystyle x$ when $\displaystyle x = 1$.

**Answers:**

(i) $\displaystyle y = 6(5 - 2x)^{-1}$

$\displaystyle \frac{dy}{dx} = 6 \times -1(5 - 2x)^{-1-1} \times (-2)$

$\displaystyle \frac{dy}{dx} = 12(5 - 2x)^{-2}$

Is this right?