Question

The slope of the normal to the curve y = 2 x 2 + 3 sin x at x = 0 is (A) 3 (B) (C) −3 (D)

Answer 1

The given equation of curve is,

y=2 x 2 +3sinx

The equation of slope of the tangent to the curve at x=0 is,

( dy dx ) x=0 = ( 4x+3cosx ) x=0 =0+3cos0 =3

The equation of slope of the normal to the curve is,

slope of normal= −1 slope of tangent

For the given curve, equation of slope of the normal is,

slope of normal= −1 3

Thus, the correct option is (D).