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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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
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
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