where does f(x)=sinx+cosx have horizontal tangent lines?

Question

How can you find out how many tangent lines this function has and what they are?

Answer 1

The horizontal tangent occurs where the first derivative equals zero.

 

f′(x) = d/dx (sinx + cosx)

f′(x) = d/dx (sinx) + d/dx(cosx)

f′(x) = cosx - sinx

0 = cosx - sinx

sinx = cosx

 

x = (π +k2π)/4