Question

For the curve y² = 2x³ – 7, the slope of the normal at (2, 3) is ______.

Options

• 4

• – 4

• `1/4`

• `(-1)/4`

Answer 1

For the curve y² = 2x³ – 7, the slope of the normal at (2, 3) is `underlinebb((-1)/4)`.

Explanation:

Curve y² = 2x³ – 7

Differentiate w.r.t. to 'x'

`2y dy/dx` = 2 × 3x² – 0

`dy/dx = (3x^2)/y`

`\implies (dy/dx)_((2","  3)) = (3 xx 2^2)/3` = 4

∵ Slope of normal = `(-1)/(dy/dx)_((2","  3))`

= `(-1)/4`