Calculus Question: If I take the derivative of a function, and plot those critical points, do I test a number from each interval into the y' function

6 years agoyou mean to find increasing/decreasing intervals? yes

6 years agoyes, to find inc and dec

6 years agoyes.

6 years agothanks guys

6 years agowell for your info, if you plug values into y'', you will know whether the graph trend is concave upwards or downwards. that will help you in sketching graph too.

6 years agothanks

6 years ago\[ y=4 x^5-45 x^4+180 x^3-310 x^2+240 x\\ y'= 20 x^4-180 x^3+540 x^2-620 x+240=\\ y'=20 (x-4) (x-3) (x-1)^2 \] You should not consider x=1 at all since (x-1)^2 is greater or equal to zero. To study the sign of y' in this case you study the sign of (x-4)(x-3) only.

6 years agowhy would we not include x=1, it is a critical number

6 years agothe whole purpose of sign analysis is that we can talk about the graph of the original function without actually graphing it, the days where technology did not exist

6 years agox=1 is a critical point. it may be a max/min point. once you plug into y'' you will know the nature of it.

6 years agoAt x=1, you cannot have a maximum or a minimum. The derivative has the same sign before 1 and after 1. So it either increasing thru 1 or decreasing thru 1. To have a max say, f has to be increasing before 1 and decreasing after 1.

6 years agox=1 can be an inflection point. Actually it is.

6 years agoyea sorry it's not a max/min point. but if i'm nt mistaken it's an inflection point.

6 years agoyes the value of y'' changes from - to +.

6 years ago