Tangent lines? ?Find an equation of the line tangent to the following curves at the given point. y=3x + sin x ;x = 0

Solution Step 1: Given curve is y=3x +sin x ;x = 0 We have to find the equation of tangent line to the given curve at given point x=0 The equation of tangent line to the curve y=f(x) at given point (x ,y ) with slope m is given by 0 0 (yy )0= m(xx ) 0 Here we have given the point x =0 0herefore the corresponding y 0 is y 03(x )0sin (x )=0(0)+sin (0)=0 (sin (0)=0) Therefore the point is (x ,y )=(0,0) 0 0 Now to find slope dy d dx= dx(3x +sin x) d 3 d = dx (3x )+ (dxn x) 2 =3(3x )+(cos x) =(9x )+cos x Step 2 2 Therefore slope m=(9x )+cos x Slope at point (0,0) is dy = m =(9(0) )+cos (0)) =1 dx(0,0) (0,0)