The slope of the normal to the curve y = 2x² + 3sin x at x = 0 is:
(A) 3   (B) 1/3   (C) - 3   (D) - 1/3

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

For a curve y = f(x) containing the point (x₁,y₁) the equation of the tangent line to the curve at (x₁,y₁) is given by 

y − y₁ = f′(x₁) (x − x₁).

The equation of the given curve is

y = 2x² + 3 sin x

Slope of the tangent to the given curve at x = 0

dy/dx]_{x = 0} = 4x + 3 cos x]_{x = 0}

= 0 + 3 cos 0

= 3

Hence, the slope of the normal to the given curve at x = 0 is

- 1 / slope of the tangent at (x = 0)

= - 1/3

Thus, the correct option is D

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 26

The slope of the normal to the curve y = 2x² + 3sin x at x = 0 is: (A) 3 (B) 1/3 (C) - 3 (D) - 1/3

Summary:

The slope of the normal to the curve y = 2x² + 3sin x at x = 0 is -1/3. Thus, the correct option is D