# Math Help - [SOLVED] Differentiation Question

1. ## [SOLVED] Differentiation Question

Question:
The equation of a curve is $y = \frac{6}{5 - 2x}$
(i) Calculate the gradient of the curve at the point where $x = 1$
(ii) A point with coordinates $(x, y)$ moves along the curve in such a way that the rate of increase of $y$ has a constant value of $0.02$ units per second. Find the rate of increase of $x$ when $x = 1$.

Answers:

(i) $y = 6(5 - 2x)^{-1}$
$\frac{dy}{dx} = 6 \times -1(5 - 2x)^{-1-1} \times (-2)$
$\frac{dy}{dx} = 12(5 - 2x)^{-2}$

Is this right?

(ii) How can I get the rate of increase of $x$?

2. Hello ^^

Originally Posted by looi76
Question:
The equation of a curve is $y = \frac{6}{5 - 2x}$
(i) Calculate the gradient of the curve at the point where $x = 1$
(ii) A point with coordinates $(x, y)$ moves along the curve in such a way that the rate of increase of $y$ has a constant value of $0.02$ units per second. Find the rate of increase of $x$ when $x = 1$.

Answers:

(i) $y = 6(5 - 2x)^{-1}$
$\frac{dy}{dx} = 6 \times -1(5 - 2x)^{-1-1} \times (-2)$
$\frac{dy}{dx} = 12(5 - 2x)^{-2}$

Is this right?
Yes it is
Remember, you're asked the gradient where x=1

(ii) How can I get the rate of increase of $x$?
The rate of increase is 0.02 means that $\frac{d^2y}{dx^2}=0.02$ (second derivative)

The second derivative represents the speed of variation of y, so if you're asked a rate of increasing or decreasing, use this