Question

Slope of the normal to the curve \(x^{2/3} + y^{2/3} = 2\) at the point (1, 1) is

• A. -1
• B. 1
• C. 1/2
• D. -1/2

Hint:

Be careful not to confuse the slope of the tangent with the slope of the normal. After finding \(\frac{dy}{dx}\), always remember to take the negative reciprocal if the question asks for the normal's slope. A common mistake is to stop after finding the tangent's slope.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Find tangent to y=x³ at (1,1).

Step 2: Key Formula (Alternate):
Point-slope form: y-y₁=m(x-x₁). m=dy/dx at x=1.

Step 3: Detailed Explanation:
dy/dx=3x², at x=1: m=3. y-1=3(x-1) → y=3x-2 → 3x-y-2=0.

Step 4: Final Answer:
Tangent equation is 3x-y-2=0.