Question:
The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is
The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is
Updated On: Sep 15, 2023
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Solution and Explanation
The equation of the given curve is.
The slope of the tangent to the given curve at x = 0 is given by,
\(\frac{dy}{dx}\)]x=0=4x+3cosx]x-0=0+3cos0=3
Hence, the slope of the normal to the given curve at x = 0 is
\(\frac{-1}{slope\,of\,the\,tangent\,at\,x=0}\)=\(-\frac{1}{2}\).
The correct answer is D.
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Concepts Used:
Tangents and Normals
- A tangent at a degree on the curve could be a straight line that touches the curve at that time and whose slope is up to the derivative of the curve at that point. From the definition, you'll be able to deduce the way to realize the equation of the tangent to the curve at any point.
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m×n = -1
- The normal to a given curve y = f(x) at a point x = x0
- The slope ‘n’ of the normal: As the normal is perpendicular to the tangent, we have: n=-1/m
Diagram Explaining Tangents and Normal:
