How do you find the intervals of increasing and decreasing using the first derivative given #y=x^4-32x+4#?

Question

1343 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-01T01:56:42

#y# is increasing for #x>2#
#y# is decreasing for #x<2#

#y=x^4-32x+4#

#y' = 4x^3-32# [Power rule]

#y# will be increasing for #y' >0# and decreasing for #y' <0#

For increasing #y: 4x^3-32>0#
#x^3 >8 -> x>2#

For decreasing #y: 4x^3-32<0#
#x^3 <8 -> x<2#

Hence #y# is increasing for #x>2# and decreasing for #x<2#

This can be seen by the graph of #y# below.
graph{x^4-32x+4 [-56.6, 73.34, -59.57, 5.35]}