Question

The point on the curve 6y = x³ + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is ______.

Options

• (4, 11)

• (4, –11)

• (–4, 11)

• (–4, –11)

Answer 1

The point on the curve 6y = x³ + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is (4, 11).

Explanation:

Since, 6y = x³ + 2  ...(i)

and Δy = 8Δx

After differentiating on both sides of equation (i) w.r.t. x, we get

`(6dy)/(dx)` = 3x² `\implies dy/dx = 1/2 x^2`

As, Δy = `dy/dx` Δx `\implies` 8Δx = `1/2 x^2 Δx`

So, x² = 16 `\implies` x = ± 4

When x = 4, then 6y = (4)³ + 2

So, 6y = 66 `\implies` y = 11

Hence, required point is (4, 11).