Question

Find the critical points and determine if the function is increasing or decreasing on the given intervals.y = 9x^4 + 10x^3Left critical point: c1 = Right critical point: c2 =

Answer 1

`y=9x^4+10x^3`

To find the critical points, first we derivate the function:

`(dy)/(dx)=36x^3+30x^2`

dy/dx has roots x = 0 and x = -5/6.

When x < -5/6, we can check that dy/dx is negative. When -5/6 < x < 0, we can check that dy/dx is positive. And, when x > 0, we can check that dy/dx is also positive.

Therefore, y is increasing when x > -5/6 and decrasing when x < -5/6. y has inflection points at x = -5/6 and x = 0