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

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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]}

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