## Calculus (3rd Edition)

The tangent line at $x=0$ is given by $$y=1.$$
Since $y=x^3+\cos x$, then the slope at $x=0$ is given as follows $$y'=3x^2-\sin x\Longrightarrow m=y'(0)=0.$$ The equation of the tangent line at $x=0$ is given by $$y=(0)x+c=c.$$ To find $c$ we use the fact that the tangent line and the curve coincide at $x=0$, so we have $y(0)=1=c$. Hence the equaion of the tangent line at $x=0$ is given by $$y=1.$$