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