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The slope of the normal to the curve {y}={2}{x}^{{2}}+{3}sin x

Question

The slope of the normal to the curve $y = 2 x^{2} + 3$ sin x at $x = 0$ is(A) 3 (B) $\frac{1}{3}$ (C) $- 3$ (D) $- \frac{1}{3}$

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Elijah Discussed

The slope of the normal to the curve

y = 2 x^{2} + 3

sin x at

x = 0

is(A) 3 (B)

\frac{1}{3}

(C)

- 3

(D)

- \frac{1}{3}

11 mins ago

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Text solutionVerified

Solution: Slope of normal to a curve is given as,

m = - \frac{1}{\frac{d y}{d x}}

Here, equation of the curve is,

y = 2 x^{2} + 3 sin x

\Rightarrow \frac{d y}{d x} = 4 x + 3 cos x

∴ \frac{d y}{d x} ∣_{x = 0} = 4 (0) + 3 cos 0 = 3

∴

Slope of the normal

= - \frac{1}{3} .

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Question Text	The slope of the normal to the curve $y = 2 x^{2} + 3$ sin x at $x = 0$ is(A) 3 (B) $\frac{1}{3}$ (C) $- 3$ (D) $- \frac{1}{3}$
Answer Type	Text solution:1
Upvotes	150