## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 25

#### Answer

The tangent line at $x=0$ is given by $$y=1.$$

#### Work Step by Step

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 $$y=1.$$

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