Question

The equation of the normal to the curve $y=2x^2+3\sin x$ at x = 0 is .

• A. x + 3y = 0
• B. x - 3y = 0
• C. 3x - y = 0
• D. 3x + y = 0

Answer 1

The correct option is A x + 3y = 0

The equation of the given curve is $y=2x^2+3\sin x$ .....[1]
Putting x = 0 in [1], we get y = 0.
So, the point of contact is (0, 0).
Now, $y=2x^2+3\sin x\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=4x+3\cos x\Rightarrow {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{(0,0)}=3.\mathrm{So},\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{normal}\mathrm{at}\left(0,0\right)\mathrm{is}y-0=-\frac{1}{3}\left(x-0\right)\Rightarrow x+3y=0.$