also y= 4x^2 + 1/x is the above increasing or decreasing

Question

increasing and decreasing functions

Answer 1

Y' = 8X - X^-2  =  (8X³ - 1) / X²

 

y' = (2X - 1)(4X² + 2X + 1) / X²

 

Analysis of first derivative: both the denominator and the quadratic factor in numerator are always positive.

Therefore y' < 0 whenever x <½ and on that interval the function is decreasing.

The function is increasing whenever x is in (½,infinity) because the slope is positive throughout this interval.