How do you find the critical numbers of #y = cos x - sin x#?

1 Answer
Jan 5, 2018

Answer:

# x = (n-1/(4))pi#
# n=0, +-1,+-2.."integer"#

Explanation:

#y = cosx - sinx#

Take the derivative wrt x and set it to zero.

#dy/dx = -(sinx + cosx) = 0#

# rArr sinx = - cosx #
#rArr sinx/cosx = - 1 #

#rArr tan(x) = - 1 #
# x = tan^(- 1)(-1) = npi - pi/4 =(n-1/(4))pi#
# x = (n-1/(4))pi#
where # n=0, +-1,+-2.."integer"#

You can also inspect the plot of the function to verify the critical values. Click on maxima and minima of the graph to find their x values and compare to the solution.

y = cosx-sinx plot:
graph{(cosx- sinx) [-10, 10, -5, 5]}